A254966 -id:A254966 - cp's OEIS frontend

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

Colin Barker, Feb 11 2015

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.

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

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).

Cf. A000566, A003215, A254965, A254966.

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

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

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)).

A254965 Indices of centered hexagonal numbers (A003215) that are also heptagonal numbers (A000566).

Original entry on oeis.org

1, 2, 13, 34, 275, 736, 6027, 16148, 132309, 354510, 2904761, 7783062, 63772423, 170872844, 1400088535, 3751419496, 30738175337, 82360356058, 674839768869, 1808176413770, 14815736739771, 39697520746872, 325271368506083, 871537280017404, 7141154370394045

Offset: 1

Colin Barker, Feb 11 2015

Also positive integers y in the solutions to 5*x^2 - 6*y^2 - 3*x + 6*y - 2 = 0, the corresponding values of x being A254964.

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

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).

Cf. A000566, A003215, A254964, A254966.

Vec(x*(x^3+11*x^2-x-1)/((x-1)*(x^4-22*x^2+1)) + O(x^100))

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

G.f.: x*(x^3+11*x^2-x-1) / ((x-1)*(x^4-22*x^2+1)).

cp's OEIS Frontend

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

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