A133285 Indices of the centered 12-gonal numbers which are also 12-gonal number, or numbers X such that 120*X^2-120*X+36 is a square.

1, 12, 253, 5544, 121705, 2671956, 58661317, 1287877008, 28274632849, 620754045660, 13628314371661, 299202162130872, 6568819252507513, 144214821393034404, 3166157251394249365, 69511244709280451616

Offset: 1

Author

Richard Choulet, Oct 16 2007

Keywords

• nonn
• easy

Comments

Partial sums of A077422. - R. J. Mathar, Nov 27 2011

Indices of centered pentagonal numbers (A005891) which are also centered hexagonal numbers (A003215). - Colin Barker, Feb 07 2015

Links

• Colin Barker, Table of n, a(n) for n = 1..746
• Index entries for linear recurrences with constant coefficients, signature (23,-23,1).

Crossrefs

Cf. A003215, A005891, A077422, A133141, A254782.

Programs

Mathematica

Table[Cos[n*ArcCos[11]] // Round, {n, 0, 15}] // Accumulate  (* Jean-François Alcover, Dec 19 2013, after R. J. Mathar *)
LinearRecurrence[{23,-23,1},{1,12,253},20] (* Harvey P. Dale, Jul 04 2018 *)

PARI

Vec(x*(11*x-1)/((x-1)*(x^2-22*x+1)) + O(x^100)) \\ Colin Barker, Feb 07 2015

Formula

a(n+2) = 22*a(n+1)-a(n)-10 ; a(n+1)=11*a(n)-5+(120*a(n)^2-120*a(n)+36)^0.5

G.f. x*(-1+11*x) / ( (x-1)*(x^2-22*x+1) ). - R. J. Mathar, Nov 27 2011

Extensions

More terms from Paolo P. Lava, Aug 06 2008