A258442 9-gonal numbers (A001106) that are the sum of eight consecutive 9-gonal numbers.

2484, 3706711688304, 5696462668411740751524, 8754305611527549602378580888144, 13453588867526192558135312033676410914164, 20675432347037054365824241005098474993236683565584, 31773938310893899311445242803186409506547794898889170298404

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..109

Index entries for linear recurrences with constant coefficients, signature (1536796803,-1536796803,1).

Formula

a(n) = 1536796803*a(n-1) - 1536796803*a(n-2) + a(n-3).

G.f.: -36*x*(22897724*x^2-3074765843*x+69) / ((x-1)*(x^2-1536796802*x+1)).

a(n) = (16014+(92323615161-65282654344*sqrt(2))*(768398401+543339720*sqrt(2))^n+(768398401+543339720*sqrt(2))^(-n)*(92323615161+65282654344*sqrt(2)))/224. - Colin Barker, Mar 07 2016

Example

2484 is in the sequence because A001106(27) = 2484 = 111 + 154 + 204 + 261 + 325 + 396 + 474 + 559 = A001106(6) + ... + A001106(13).

Prog

(PARI) Vec(-36*x*(22897724*x^2-3074765843*x+69) / ((x-1)*(x^2-1536796802*x+1)) + O(x^20))

Crossrefs

Cf. A001106, A258441, A258443, A258444.

Sequence in context: A235546 A214477 A181258 * A255750 A255757 A254839

Adjacent sequences: A258439 A258440 A258441 * A258443 A258444 A258445

Keyword

nonn,easy

Author

Colin Barker, May 30 2015

Status

approved