A252093 Numbers n such that the pentagonal number P(n) is equal to the sum of the octagonal numbers N(m), N(m+1) and N(m+2) for some m.

90, 84515202, 79520184374490, 74820382437504220002, 70398348194603325406910490, 66237665019531059286273761843202, 62322886541476336272141806645338008090, 58639479301035764180766150529698967373864802, 55173768795323625559613033164820557197489306307290

Offset

1,1

Comments

Also nonnegative integers y in the solutions to 18*x^2-3*y^2+24*x+y+18 = 0, the corresponding values of x being A252092.

Links

Colin Barker, Table of n, a(n) for n = 1..168

Index entries for linear recurrences with constant coefficients, signature (940899,-940899,1).

Formula

a(n) = 940899*a(n-1)-940899*a(n-2)+a(n-3).

G.f.: -18*x*(489*x^2-9206*x+5) / ((x-1)*(x^2-940898*x+1)).

Example

90 is in the sequence because P(90) = 12105 = 3816+4033+4256 = N(36)+N(37)+N(38).

Prog

(PARI) Vec(-18*x*(489*x^2-9206*x+5)/((x-1)*(x^2-940898*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A000567, A252092.

Sequence in context: A028672 A172650 A353038 * A172756 A306304 A175690

Adjacent sequences: A252090 A252091 A252092 * A252094 A252095 A252096

Keyword

nonn,easy

Author

Colin Barker, Dec 14 2014

Status

approved