A253880 Triangular numbers (A000217) that are also centered heptagonal numbers (A069099).

1, 253, 64261, 16322041, 4145734153, 1053000152821, 267457893082381, 67933251842771953, 17254778510170993681, 4382645808331589623021, 1113174780537713593253653, 282742011610770921096804841, 71815357774355276244995175961, 18240818132674629395307677889253

Offset: 1

Author

Colin Barker, Jan 17 2015

Keywords

• nonn
• easy

Examples

			253 is in the sequence because it is the 22nd triangular number and the 9th centered heptagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..416
• Index entries for linear recurrences with constant coefficients, signature (254,-1).

Crossrefs

Cf. A000217, A069099, A253878, A253879.

Similar sequences of the type cosh((2*m+1)*arccosh(k))/k are listed in A302329. This is the case k=8.

Programs

Mathematica

LinearRecurrence[{254,-1},{1,253},20] (* Harvey P. Dale, May 17 2017 *)

PARI

Vec(-x*(x-1)/(x^2-254*x+1) + O(x^100))

Formula

a(n) = 254*a(n-1) - a(n-2).

G.f.: -x*(x-1) / (x^2 - 254*x + 1).

a(n) = (1/8)*T(2*n-1, 8), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - Peter Bala, Jul 08 2022