A252092 Numbers n such that the sum of the octagonal numbers N(n), N(n+1) and N(n+2) is equal to the pentagonal number P(m) for some m.

36, 34503186, 32463979328256, 30545293221963537966, 28740005301926584966432476, 27041413508541574648524420892746, 25443211887331010498345403984177120696, 23939467178338931702363652343255760088359526, 22524596789139300949003224751966312751633124800916

Offset

1,1

Comments

Also nonnegative integers x in the solutions to 18*x^2-3*y^2+24*x+y+18 = 0, the corresponding values of y being A252093.

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.: 6*x*(599*x^2-105137*x-6) / ((x-1)*(x^2-940898*x+1)).

Example

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

Prog

(PARI) Vec(6*x*(599*x^2-105137*x-6)/((x-1)*(x^2-940898*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A000567, A252093.

Sequence in context: A134369 A151654 A135240 * A307949 A058432 A058458

Adjacent sequences: A252089 A252090 A252091 * A252093 A252094 A252095

Keyword

nonn,easy

Author

Colin Barker, Dec 14 2014

Status

approved