1,1

The sequence has been extended to n=1 using the recurrence. - Andrew Howroyd, May 25 2025

Andrew Howroyd, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, Goldberg Graph.

Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set.

Index entries for linear recurrences with constant coefficients, signature (4,23,113,52,385,-862,518,64,-651,-102,79,970,300,-469,-343,-72,46,65,-8,-4).

G.f.: x*(4 + 46*x + 339*x^2 + 208*x^3 + 1925*x^4 - 5172*x^5 + 3626*x^6 + 512*x^7 - 5859*x^8 - 1020*x^9 + 869*x^10 + 11640*x^11 + 3900*x^12 - 6566*x^13 - 5145*x^14 - 1152*x^15 + 782*x^16 + 1170*x^17 - 152*x^18 - 80*x^19)/((1 - x + 6*x^2 - 11*x^3 + 7*x^4 - 6*x^5 + 7*x^6 - 2*x^7)*(1 - 3*x - 32*x^2 - 116*x^3 - 16*x^4 - 30*x^5 - 149*x^6 - 20*x^7 + 114*x^8 + 108*x^9 + 49*x^10 - 11*x^12 - 2*x^13)). - Andrew Howroyd, May 25 2025

a(n) = 4*a(n-1)+23*a(n-2)+113*a(n-3)+52*a(n-4)+385*a(n-5)-862*a(n-6)+518*a(n-7)+64*a(n-8)-651*a(n-9)-102*a(n-10)+79*a(n-11)+970*a(n-12)+300*a(n-13)-469*a(n-14)-343*a(n-15)-72*a(n-16)+46*a(n-17)+65*a(n-18)-8*a(n-19)-4*a(n-20). - Eric W. Weisstein, Sep 03 2025

LinearRecurrence[{4, 23, 113, 52, 385, -862, 518, 64, -651, -102, 79, 970, 300, -469, -343, -72, 46, 65, -8, -4}, {4, 62, 679, 4802, 43964, 362621, 3063638, 26023026, 219108064, 1853148122, 15656192182, 132249149729, 1117453853962, 9440565205028, 79760002749149, 673865612643090, 5693211039917562, 48099847738288178, 406377235046133496, 3433326098510195722}, 25] (* Eric W. Weisstein, Sep 03 2025 *)

CoefficientList[Series[(4 + 46 x + 339 x^2 + 208 x^3 + 1925 x^4 - 5172 x^5 + 3626 x^6 + 512 x^7 - 5859 x^8 - 1020 x^9 + 869 x^10 + 11640 x^11 + 3900 x^12 - 6566 x^13 - 5145 x^14 - 1152 x^15 + 782 x^16 + 1170 x^17 - 152 x^18 - 80 x^19)/((1 - x + 6 x^2 - 11 x^3 + 7 x^4 - 6 x^5 + 7 x^6 - 2 x^7) (1 - 3 x - 32 x^2 - 116 x^3 - 16 x^4 - 30 x^5 - 149 x^6 - 20 x^7 + 114 x^8 + 108 x^9 + 49 x^10 - 11 x^12 - 2 x^13)), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 03 2025 *)

Cf. A366515.

Sequence in context: A232156 A316391 A293968 * A222791 A166028 A359620

Adjacent sequences: A374553 A374554 A374555 * A374557 A374558 A374559

nonn,easy

Eric W. Weisstein, Jul 11 2024

a(13) from Eric W. Weisstein, Aug 24 2024

a(1)-a(2) and a(14) onwards from Andrew Howroyd, May 25 2025

approved