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

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..416

Index entries for linear recurrences with constant coefficients, signature (254,-1).

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

Example

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

Mathematica

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

Prog

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

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.

Sequence in context: A176087 A006060 A077695 * A145628 A237419 A363866

Adjacent sequences: A253877 A253878 A253879 * A253881 A253882 A253883

Keyword

nonn,easy

Author

Colin Barker, Jan 17 2015

Status

approved