A253689 Centered triangular numbers (A005448) which are also centered heptagonal numbers (A069099).

1, 316, 7246, 3818431, 87657571, 46195373386, 1060481282176, 558871623400861, 12829702464103141, 6761228853708238456, 155213739350238513106, 81797346113290645435291, 1877775805829483067448711, 989584286517361374767907526, 22717331543711346799755988036

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..490

Index entries for linear recurrences with constant coefficients, signature (1,12098,-12098,-1,1).

Formula

a(n) = a(n-1)+12098*a(n-2)-12098*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+315*x^3-5168*x^2+315*x+1) / ((x-1)*(x^2-110*x+1)*(x^2+110*x+1)).

Example

316 is in the sequence because it is the 15th centered triangular number and the 10th centered heptagonal number.

Mathematica

LinearRecurrence[{1, 12098, -12098, -1, 1}, {1, 316, 7246, 3818431, 87657571}, 20] (* or *) CoefficientList[Series[(x^4 + 315 x^3 - 5168 x^2 + 315 x + 1) / ((1 - x) (x^2 - 110 x + 1)(x^2 + 110 x + 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Jan 10 2015 *)

Prog

(PARI) Vec(-x*(x^4+315*x^3-5168*x^2+315*x+1)/((x-1)*(x^2-110*x+1)*(x^2+110*x+1)) + O(x^100))
(Magma) I:=[1, 316, 7246, 3818431, 87657571]; [n le 5 select I[n] else  Self(n-1)+12098*Self(n-2)-12098*Self(n-3)-Self(n-4)+Self(n-5): n in [1..20]]; // Vincenzo Librandi, Jan 10 2015

Crossrefs

Cf. A005448, A069099, A253476, A253477.

Sequence in context: A237561 A358926 A264540 * A233048 A101112 A012871

Adjacent sequences: A253686 A253687 A253688 * A253690 A253691 A253692

Keyword

nonn,easy

Author

Colin Barker, Jan 09 2015

Status

approved