A254857 -id:A254857 - cp's OEIS frontend

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

Colin Barker, Feb 08 2015

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.

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

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).

Cf. A000567, A069099, A254856, A254857.

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

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

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)).

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

Original entry on oeis.org

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

Colin Barker, Feb 08 2015

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.

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

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).

Cf. A000567, A069099, A254855, A254857.

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

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

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)).

cp's OEIS Frontend

A254855 Indices of octagonal numbers (A000567) that are also centered heptagonal numbers (A069099).

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