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

Author

Colin Barker, Jan 09 2015

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Cf. A005448, A069099, A253476, A253477.

Programs

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

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 *)

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))

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)).