%I #16 May 24 2025 19:00:56

%S 12,100,1588,15978,179972,1809558,18324824,181378366,1782805552,

%T 17363990448,168057761164,1617180377184,15486675862236,

%U 147673946969116,1402890497740544,13283057055815430,125395241075209800,1180599951439852770,11088548750458808244,103918533147459728842

%N Number of (non-null) connected induced subgraphs in the n-flower graph.

%C 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 24 2025

%H Andrew Howroyd, <a href="/A362807/b362807.txt">Table of n, a(n) for n = 1..200</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FlowerGraph.html">Flower Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>.

%H <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (22,-150,226,1112,-5450,11884,-6878, -44971,146976,-284908,407972, -438909,443802,14624,-1169814,2380928, -2419194,370978,306798,-41711,3516276, -7451820,4641152,6836032,-10088448,-1251200, 4632064,258560,-217088,-462848, -204800,86016,16384,16384).

%F a(n) = 16^n - A362793(n) - 1.

%F G.f.: x*(12 - 164*x + 1188*x^2 - 6670*x^3 + 30712*x^4 - 157814*x^5 + 535856*x^6 - 1226534*x^7 + 1551888*x^8 + 4984*x^9 - 4575116*x^10 + 13495862*x^11 - 21808180*x^12 + 20106522*x^13 - 11358320*x^14 + 10928178*x^15 - 30026404*x^16 + 58877492*x^17 - 21768152*x^18 - 120536708*x^19 + 215936116*x^20 - 192382876*x^21 + 129015952*x^22 + 33170240*x^23 - 144954048*x^24 + 31882112*x^25 - 5940992*x^26 + 18928640*x^27 + 3677184*x^28 + 2224128*x^29 - 872448*x^30 - 335872*x^31 + 32768*x^32 + 49152*x^33)/((1 - x)^3*(1 + x)^3*(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 24 2025

%Y Cf. A362793 (number of vertex cuts).

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, May 04 2023

%E a(1)-a(4) and a(8) onwards from _Andrew Howroyd_, May 24 2025