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%I #22 Jan 02 2024 08:54:27
%S 1,12,253,5544,121705,2671956,58661317,1287877008,28274632849,
%T 620754045660,13628314371661,299202162130872,6568819252507513,
%U 144214821393034404,3166157251394249365,69511244709280451616
%N 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.
%C Partial sums of A077422. - _R. J. Mathar_, Nov 27 2011
%C Indices of centered pentagonal numbers (A005891) which are also centered hexagonal numbers (A003215). - _Colin Barker_, Feb 07 2015
%H Colin Barker, <a href="/A133285/b133285.txt">Table of n, a(n) for n = 1..746</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (23,-23,1).
%F 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
%F G.f. x*(-1+11*x) / ( (x-1)*(x^2-22*x+1) ). - _R. J. Mathar_, Nov 27 2011
%t Table[Cos[n*ArcCos[11]] // Round, {n, 0, 15}] // Accumulate (* _Jean-François Alcover_, Dec 19 2013, after _R. J. Mathar_ *)
%t LinearRecurrence[{23,-23,1},{1,12,253},20] (* _Harvey P. Dale_, Jul 04 2018 *)
%o (PARI) Vec(x*(11*x-1)/((x-1)*(x^2-22*x+1)) + O(x^100)) \\ _Colin Barker_, Feb 07 2015
%Y Cf. A003215, A005891, A077422, A133141, A254782.
%K nonn,easy
%O 1,2
%A _Richard Choulet_, Oct 16 2007
%E More terms from _Paolo P. Lava_, Aug 06 2008
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