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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
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
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
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 *)
PROG
(PARI) Vec(x*(11*x-1)/((x-1)*(x^2-22*x+1)) + O(x^100)) \\ Colin Barker, Feb 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Richard Choulet, Oct 16 2007
EXTENSIONS
More terms from Paolo P. Lava, Aug 06 2008
STATUS
approved