A254856 Indices of centered heptagonal numbers (A069099) that are also octagonal numbers (A000567).

1, 2, 15, 40, 377, 1026, 9775, 26624, 253761, 691186, 6587999, 17944200, 171034201, 465858002, 4440301215, 12094363840, 115276797377, 313987601826, 2992756430575, 8151583283624, 77696390397561, 211627177772386, 2017113393905999, 5494155038798400

Offset

1,2

Comments

Also positive integers y in the solutions to 6*x^2 - 7*y^2 - 4*x + 7*y - 2 = 0, the corresponding values of x being A254855.

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^3+13*x^2-x-1) / ((x-1)*(x^4-26*x^2+1)).

Example

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

Mathematica

LinearRecurrence[{1, 26, -26, -1, 1}, {1, 2, 15, 40, 377}, 30] (* Harvey P. Dale, Apr 30 2019 *)

Prog

(PARI) Vec(x*(x^3+13*x^2-x-1)/((x-1)*(x^4-26*x^2+1)) + O(x^100))

Crossrefs

Cf. A000567, A069099, A254855, A254857.

Sequence in context: A200156 A249997 A032016 * A001007 A300393 A152015

Adjacent sequences: A254853 A254854 A254855 * A254857 A254858 A254859

Keyword

nonn,easy

Author

Colin Barker, Feb 08 2015

Status

approved