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A081065 Numbers n such that n^2 = (1/3)*(n+floor(sqrt(3)*n*floor(sqrt(3)*n))). 2

%I #26 Mar 14 2016 20:02:48

%S 2,24,330,4592,63954,890760,12406682,172802784,2406832290,33522849272,

%T 466913057514,6503259955920,90578726325362,1261598908599144,

%U 17571805994062650,244743685008277952,3408839784121828674,47479013292697323480,661297346313640700042

%N Numbers n such that n^2 = (1/3)*(n+floor(sqrt(3)*n*floor(sqrt(3)*n))).

%C a(n)/2 gives indices of pentagonal numbers which are also triangular.

%C a(n) itself gives x-values solving the Diophantine equation 2*x^2 + (x-1)^2 = y^2.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-15,1).

%F a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3).

%F a(n) = 14*a(n-1) - a(n-2) - 4. [_Sture Sjöstedt_, May 02 2011]

%F G.f.: 2*(1-3*x)/((1-x)*(1-14*x+x^2)). - _Bruno Berselli_, Nov 11 2011

%t LinearRecurrence[{15,-15,1},{2,24,330},20] (* _Harvey P. Dale_, Mar 14 2016 *)

%o (PARI) Vec(2*(1-3*x)/((1-x)*(1-14*x+x^2)) + O(x^40)) \\ _Michel Marcus_, Nov 17 2014

%Y Cf. A046090, A046174, A046175.

%K nonn,easy

%O 1,1

%A _Benoit Cloitre_, Apr 15 2003

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)