OFFSET
1,1
COMMENTS
The sequence has been extended to n=1 using the recurrence. - Andrew Howroyd, May 25 2025
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Goldberg Graph.
Eric Weisstein's World of Mathematics, Graph Cycle.
Index entries for linear recurrences with constant coefficients, signature (51,-1065,11745,-73158, 249464,-357075, -335315,1866969,-1818741, -1114430, 2775900,-671320,-972704,350080,89600).
FORMULA
G.f.: x*(11 - 258*x + 950*x^2 + 18327*x^3 - 186444*x^4 + 574466*x^5 - 93117*x^6 - 2799252*x^7 + 4600196*x^8 - 204095*x^9 - 3601380*x^10 + 836148*x^11 + 103680*x^12 + 866880*x^13 + 268800*x^14)/((1 - x)^2*(1 + x)*(1 - 2*x)*(1 - 4*x)*(1 - 7*x)*(1 - 10*x)^2*(1 - x - x^2)*(1 - x - 4*x^2)*(1 - 15*x + 19*x^2 + 4*x^3)). - Andrew Howroyd, May 25 2025
MATHEMATICA
LinearRecurrence[{51, -1065, 11745, -73158, 249464, -357075, -335315, 1866969, -1818741, -1114430, 2775900, -671320, -972704, 350080, 89600}, {11, 303, 4688, 63915, 834498, 10702179, 136354380, 1736343975, 22177076066, 284685012897, 3676879664312, 47798333570337, 625348433657826, 8230570229973093, 108913174529029104}, 20] (* Eric W. Weisstein, Aug 28 2025 *)
CoefficientList[Series[(11 - 258 x + 950 x^2 + 18327 x^3 - 186444 x^4 + 574466 x^5 - 93117 x^6 - 2799252 x^7 + 4600196 x^8 - 204095 x^9 - 3601380 x^10 + 836148 x^11 + 103680 x^12 + 866880 x^13 + 268800 x^14)/((1 - x)^2 (1 + x) (1 - 2 x) (1 - 4 x) (1 - 7 x) (1 - 10 x)^2 (1 - x - x^2) (1 - x - 4 x^2) (1 - 15 x + 19 x^2 + 4 x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 28 2025 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 16 2023
EXTENSIONS
a(1)-a(2) and a(9) onwards from Andrew Howroyd, May 25 2025
STATUS
approved