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A133273 Indices of centered decagonal numbers which are also decagonal numbers. 3

%I

%S 1,10,171,3060,54901,985150,17677791,317215080,5692193641,

%T 102142270450,1832868674451,32889493869660,590178020979421,

%U 10590314883759910,190035489886698951,3410048503076821200,61190837565496082641,1098025027675852666330,19703259660599851911291

%N Indices of centered decagonal numbers which are also decagonal numbers.

%C Numbers k such that 80*k^2 - 80*k + 25 is a square.

%C Also the indices of centered square numbers which are also centered pentagonal numbers. - _Colin Barker_, Jan 01 2015

%H Colin Barker, <a href="/A133273/b133273.txt">Table of n, a(n) for n = 1..798</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (19,-19,1).

%F a(n+2) = 18*a(n+1) - a(n) - 8.

%F a(n+1) = 9*a(n) - 4 + sqrt(80*a(n)^2 - 80*a(n) + 25).

%F G.f.: x*(-1+9*x)/(-1+x)/(1 - 18*x + x^2). - _R. J. Mathar_, Nov 14 2007

%F a(n) = (1/2) - (1/8)*sqrt(5)*{[9-4*sqrt(5)]^n - [9+4*sqrt(5)]^n} + (1/4)*{[9-4*sqrt(5)]^n + [9+4*sqrt(5)]^n}, with n>=0. - _Paolo P. Lava_, Nov 25 2008

%F a(n) = 19*a(n-1) - 19*a(n-2) + a(n-3). - _Colin Barker_, Jan 01 2015

%o (PARI) Vec(x*(-1+9*x)/((-1+x)*(1-18*x+x^2)) + O(x^100)) \\ _Colin Barker_, Jan 01 2015

%Y Cf. A128922.

%K nonn,easy

%O 1,2

%A _Richard Choulet_, Oct 16 2007

%E More terms from _Paolo P. Lava_, Nov 25 2008

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Last modified September 17 16:57 EDT 2019. Contains 327136 sequences. (Running on oeis4.)