A254965 -id:A254965 - 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)).

A254966 Heptagonal numbers (A000566) that are also centered hexagonal numbers (A003215).

Original entry on oeis.org

1, 7, 469, 3367, 226051, 1622881, 108956107, 782225269, 52516617517, 377030956771, 25312900687081, 181728138938347, 12200765614555519, 87592585937326477, 5880743713315073071, 42219444693652423561, 2834506269052250664697, 20349684749754530829919

Offset: 1

Colin Barker, Feb 11 2015

			469 is in the sequence because it is the 14th heptagonal number and the 13th centered hexagonal number.

Colin Barker, Table of n, a(n) for n = 1..746
Index entries for linear recurrences with constant coefficients, signature (1,482,-482,-1,1).

Cf. A000566, A003215, A254964, A254965.

LinearRecurrence[{1,482,-482,-1,1},{1,7,469,3367,226051},20] (* Harvey P. Dale, May 17 2019 *)

Vec(-x*(x^4+6*x^3-20*x^2+6*x+1)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100))

a(n) = a(n-1)+482*a(n-2)-482*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+6*x^3-20*x^2+6*x+1) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)).

cp's OEIS Frontend

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

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