A254855 Indices of octagonal numbers (A000567) that are also centered heptagonal numbers (A069099).

1, 2, 16, 43, 407, 1108, 10558, 28757, 274093, 746566, 7115852, 19381951, 184738051, 503184152, 4796073466, 13063405993, 124513172057, 339145371658, 3232546400008, 8804716257107, 83921693228143, 228583477313116, 2178731477531702, 5934365693883901

Offset: 1

Author

Colin Barker, Feb 08 2015

Keywords

• nonn
• easy

Comments

Also positive integers x in the solutions to 6*x^2 - 7*y^2 - 4*x + 7*y - 2 = 0, the corresponding values of y being A254856.

Examples

			16 is in the sequence because the 16th octagonal number is 736, which is also the 15th centered heptagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,26,-26,-1,1).

Crossrefs

Cf. A000567, A069099, A254856, A254857.

Programs

Mathematica

LinearRecurrence[{1,26,-26,-1,1},{1,2,16,43,407},30] (* Harvey P. Dale, Aug 31 2021 *)

PARI

Vec(-x*(x^4+x^3-12*x^2+x+1)/((x-1)*(x^4-26*x^2+1)) + O(x^100))

Formula

a(n) = a(n-1)+26*a(n-2)-26*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+x^3-12*x^2+x+1) / ((x-1)*(x^4-26*x^2+1)).