A133272 Indices of centered heptagonal numbers (A069099) which are also heptagonal numbers (A000566).

1, 7, 78, 924, 11005, 131131, 1562562, 18619608, 221872729, 2643853135, 31504364886, 375408525492, 4473397941013, 53305366766659, 635191003258890, 7568986672340016, 90192649064821297, 1074742802105515543

Offset: 1

Author

Richard Choulet, Oct 16 2007

Keywords

• nonn
• easy

Comments

Numbers X such that 140*X^2-140*X+49 is a square.

Also positive integers x in the solutions to 5*x^2 - 7*y^2 - 5*x + 7*y = 0, the corresponding values of y being A253621. - Colin Barker, Jan 06 2015

Also indices of centered pentagonal numbers (A005891) which are also centered heptagonal numbers (A069099). - Colin Barker, Jan 06 2015

Links

• Colin Barker, Table of n, a(n) for n = 1..930
• Index entries for linear recurrences with constant coefficients, signature (13,-13,1).

Crossrefs

Cf. A000566, A069099, A128919, A253621, A253622.

Programs

Mathematica

LinearRecurrence[{13,-13,1},{1,7,78},25] (* Paolo Xausa, Jan 07 2024 *)

PARI

Vec(x*(6*x-1)/((x-1)*(x^2-12*x+1)) + O(x^100)) \\ Colin Barker, Jan 06 2015

Formula

a(n+2) = 12*a(n+1) - a(n) - 5.

a(n+1) = 6*a(n) - 5/2 + (1/2)*sqrt(140*a(n)^2 - 140*a(n) + 49).

G.f.: x*(-1+6*x)/((-1+x)*(1-12*x+x^2)). - R. J. Mathar, Nov 14 2007

a(n) = 13*a(n-1) - 13*a(n-2) + a(n-3). - Colin Barker, Jan 06 2015

Extensions

More terms from Paolo P. Lava, Jul 14 2008