A254964 Indices of heptagonal numbers (A000566) that are also centered hexagonal numbers (A003215).

1, 2, 14, 37, 301, 806, 6602, 17689, 144937, 388346, 3182006, 8525917, 69859189, 187181822, 1533720146, 4109474161, 33671984017, 90221249714, 739249928222, 1980758019541, 16229826436861, 43486455180182, 356316931682714, 954721255944457, 7822742670582841

Offset

1,2

Comments

Also positive integers x in the solutions to 5*x^2 - 6*y^2 - 3*x + 6*y - 2 = 0, the corresponding values of y being A254965.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,22,-22,-1,1).

Formula

a(n) = a(n-1)+22*a(n-2)-22*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^2-3*x+1)*(x^2+4*x+1) / ((x-1)*(x^4-22*x^2+1)).

Example

14 is in the sequence because the 14th heptagonal number is 469, which is also the 13th centered hexagonal number.

Mathematica

LinearRecurrence[{1, 22, -22, -1, 1}, {1, 2, 14, 37, 301}, 30] (* Harvey P. Dale, Apr 13 2018 *)

Prog

(PARI) Vec(-x*(x^2-3*x+1)*(x^2+4*x+1)/((x-1)*(x^4-22*x^2+1)) + O(x^100))

Crossrefs

Cf. A000566, A003215, A254965, A254966.

Sequence in context: A338327 A322226 A218546 * A108597 A062548 A067293

Adjacent sequences: A254961 A254962 A254963 * A254965 A254966 A254967

Keyword

nonn,easy

Author

Colin Barker, Feb 11 2015

Status

approved