A252116 Numbers n such that the pentagonal number P(n) is equal to the sum of the heptagonal numbers H(m), H(m+1) and H(m+2) for some m.

1283, 60266, 133006667, 6248482130, 13790397229331, 647855124125114, 1429815965398472795, 67170914973291570338, 148246178910654059084579, 6964414805612961471642122, 15370460320384618188608829803, 722084455808392156329506905586

Offset

1,1

Comments

Also nonnegative integers y in the solutions to 15*x^2-3*y^2+21*x+y+16 = 0, the corresponding values of x being A252115.

Links

Colin Barker, Table of n, a(n) for n = 1..398

Index entries for linear recurrences with constant coefficients, signature (1,103682,-103682,-1,1).

Formula

G.f.: -x*(2*x^4+57*x^3-77605*x^2+58983*x+1283) / ((x-1)*(x^2-322*x+1)*(x^2+322*x+1)).

Example

1283 is in the sequence because P(1283) = 2468492 = 819963+822829+825700 = H(573)+H(574)+H(575).

Mathematica

LinearRecurrence[{1, 103682, -103682, -1, 1}, {1283, 60266, 133006667, 6248482130, 13790397229331}, 20] (* Harvey P. Dale, May 08 2020 *)

Prog

(PARI) Vec(-x*(2*x^4+57*x^3-77605*x^2+58983*x+1283)/((x-1)*(x^2-322*x+1)*(x^2+322*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A000566, A252115.

Sequence in context: A170784 A269826 A270055 * A084803 A104399 A353347

Adjacent sequences: A252113 A252114 A252115 * A252117 A252118 A252119

Keyword

nonn,easy

Author

Colin Barker, Dec 14 2014

Status

approved