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

1,2

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.

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).

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)).

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000567, A069099, A254856, A254857.

Sequence in context: A211620 A023638 A139267 * A181340 A275032 A295533

Adjacent sequences: A254852 A254853 A254854 * A254856 A254857 A254858

Keyword

nonn,easy

Author

Colin Barker, Feb 08 2015

Status

approved