1,1

The n-flower graph can be defined without using parallel edges for n >= 3. It is a snark for odd n >= 5. The sequence has been extended to n=1 using the recurrence. - Andrew Howroyd, May 26 2025

Eric W. Weisstein, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, Flower Graph.

Eric Weisstein's World of Mathematics, Vertex Cut.

Index entries for linear recurrences with constant coefficients, signature (38,-502,2626,-2504,-23242,99084, -197022,65077,866512,-2636524, 4966500,-6966461,7466346, -7086208,-1403798,21097952, -40514042,39078082,-5628850, -4950479,4183652,-63712236,123870272, -67422400,-119464960,160163968, 24651264,-73854464,-4354048,3010560, 7200768,3362816,-1359872,-245760,-262144).

a(n) = 16^n - A362807(n) - 1.

G.f.: x*(3 + 41*x - 1877*x^2 + 24223*x^3 - 155567*x^4 + 712821*x^5 - 3175525*x^6 + 9788755*x^7 - 20513342*x^8 + 23283674*x^9 + 7386930*x^10 - 90085228*x^11 + 240938097*x^12 - 372498307*x^13 + 329382407*x^14 - 178794353*x^15 + 183030277*x^16 - 524859021*x^17 + 972684289*x^18 - 223479429*x^19 - 2139623484*x^20 + 3599516552*x^21 - 3143208848*x^22 + 2025400832*x^23 + 567453248*x^24 - 2308044800*x^25 + 577924864*x^26 - 121595392*x^27 + 287691776*x^28 + 48377856*x^29 + 35168256*x^30 - 11841536*x^31 - 4915200*x^32 + 720896*x^33 + 786432*x^34)/((1 - x)^3*(1 + x)^3*(1 - 16*x)*(1 - 5*x + 9*x^2 - 10*x^3 + 4*x^4)^2*(1 + 5*x + 9*x^2 + 10*x^3 + 4*x^4)^2*(1 - 11*x + 23*x^2 - 47*x^3 + 46*x^4 + 4*x^5 + 8*x^6)^2). - Andrew Howroyd, May 26 2025

a(n) = 38*a(n-1)-502*a(n-2)+2626*a(n-3)-2504*a(n-4)-23242*a(n-5)+99084*a(n-6)-197022*a(n-7)+65077*a(n-8)+866512*a(n-9)-2636524*a(n-10)+4966500*a(n-11)-6966461*a(n-12)+7466346*a(n-13)-7086208*a(n-14)-1403798*a(n-15)+21097952*a(n-16)-40514042*a(n-17)+39078082*a(n-18)-5628850*a(n-19)-4950479*a(n-20)+4183652*a(n-21)-63712236*a(n-22)+123870272*a(n-23)-67422400*a(n-24)-119464960*a(n-25)+160163968*a(n-26)+24651264*a(n-27)-73854464*a(n-28)-4354048*a(n-29)+3010560*a(n-30)+7200768*a(n-31)+3362816*a(n-32)-1359872*a(n-33)-245760*a(n-34)-262144*a(n-35). - Eric W. Weisstein, Sep 03 2025

LinearRecurrence[{38, -502, 2626, -2504, -23242, 99084, -197022, 65077, 866512, -2636524, 4966500, -6966461, 7466346, -7086208, -1403798, 21097952, -40514042, 39078082, -5628850, -4950479, 4183652, -63712236, 123870272, -67422400, -119464960, 160163968, 24651264, -73854464, -4354048, 3010560, 7200768, 3362816, -1359872, -245760, -262144}, {3, 155, 2507, 49557, 868603, 14967657, 250110631, 4113588929, 66936671183, 1082147637327, 17424128283251, 279857796333471, 4488112951508259, 71909920090958819, 1151518614109106431, 18433461016653736185, 295022509938277616055, 4721185882918205360925, 75546775177163864610891, 1208821901081481714977333, 19341841169997004054577291, 309475935958937922080789499, 4951675588326557038622943063, 79227375555342637141299625083, 1267643287692004799145563024543, 20282341745331764880368541105263, 324517924735306950255673372568867, 5192291036327955494815840755293133, 83076695896436374806078906025777395, 1329227498411733027219875882595666513, 21267643342232242137209772714612275375, 340282324594262049869091150715072404713, 5444517480778138855031558186689045991559, 87112282341951119987780630846169504181095, 1393796541886621068301465324629031900715259}, 40] (* Eric W. Weisstein, Sep 03 2025 *)

CoefficientList[Series[(3 + 41 x - 1877 x^2 + 24223 x^3 - 155567 x^4 + 712821 x^5 - 3175525 x^6 + 9788755 x^7 - 20513342 x^8 + 23283674 x^9 + 7386930 x^10 - 90085228 x^11 + 240938097 x^12 - 372498307 x^13 + 329382407 x^14 - 178794353 x^15 + 183030277 x^16 - 524859021 x^17 + 972684289 x^18 - 223479429 x^19 - 2139623484 x^20 + 3599516552 x^21 - 3143208848 x^22 + 2025400832 x^23 + 567453248 x^24 - 2308044800 x^25 + 577924864 x^26 - 121595392 x^27 + 287691776 x^28 + 48377856 x^29 + 35168256 x^30 - 11841536 x^31 - 4915200 x^32 + 720896 x^33 + 786432 x^34)/((1 - x)^3 (1 + x)^3 (1 - 16 x) (1 - 5 x + 9 x^2 - 10 x^3 + 4 x^4)^2 (1 + 5 x + 9 x^2 + 10 x^3 + 4 x^4)^2 (1 - 11 x + 23 x^2 - 47 x^3 + 46 x^4 + 4 x^5 + 8 x^6)^2), {x, 0, 40}], x] (* Eric W. Weisstein, Sep 03 2025 *)

Cf. A362807 (number of connected induced subgraphs).

Sequence in context: A344898 A327058 A087306 * A278877 A203682 A316479

Adjacent sequences: A362790 A362791 A362792 * A362794 A362795 A362796

nonn,easy

Eric W. Weisstein, May 04 2023

a(1)-a(4) and a(8) onwards from Andrew Howroyd, May 26 2025

approved