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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. 4
1, 12, 253, 5544, 121705, 2671956, 58661317, 1287877008, 28274632849, 620754045660, 13628314371661, 299202162130872, 6568819252507513, 144214821393034404, 3166157251394249365, 69511244709280451616 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

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

a(n) = (1/2)+(1/4)*[11+2*sqrt(30)]^n+(1/20)*[11+2*sqrt(30)]^n*sqrt(30)+(1/4)*[11-2*sqrt(30)]^n -(1/20)*sqrt(30)*[11-2*sqrt(30)]^n, with n>=0. - Paolo P. Lava, Aug 06 2008

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

MATHEMATICA

Table[Cos[n*ArcCos[11]] // Round, {n, 0, 15}] // Accumulate  (* Jean-Fran├žois Alcover, Dec 19 2013, after R. J. Mathar *)

LinearRecurrence[{23, -23, 1}, {1, 12, 253}, 20] (* Harvey P. Dale, Jul 04 2018 *)

PROG

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

CROSSREFS

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

Sequence in context: A065583 A129585 A034672 * A239778 A113091 A053324

Adjacent sequences:  A133282 A133283 A133284 * A133286 A133287 A133288

KEYWORD

nonn,easy

AUTHOR

Richard Choulet, Oct 16 2007

EXTENSIONS

More terms from Paolo P. Lava, Aug 06 2008

STATUS

approved

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Last modified March 30 06:59 EDT 2020. Contains 333119 sequences. (Running on oeis4.)