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A101180 Numbers n such that 19*n^2 + 19*n + 1 is a square. 3

%I #19 Jun 13 2015 00:51:37

%S 0,8,671,15639,42159,981911,77624048,1807894920,4873553880,

%T 113507005568,8973184757831,208989037004319,563373081435879,

%U 13121182828725551,1037282211558181688,24158714697817430640,65124801462951244560,1516782492521509296728

%N Numbers n such that 19*n^2 + 19*n + 1 is a square.

%C Define a(1)=0, a(2)=8, a(3)=671, a(4)=15639, a(5)=42159, a(6)=981911, the first 6 terms found for the sequence then a(7)=57799*(2*a(3)+1)-a(2)-1, a(8)=57799*(2*a(4)+1)-a(1)-1 for n>8 a(n)=57799*(2*a(n-4)+1)-a(n-8)-1 remark:57799 = 38*39*39+1 =2*19*(39^2)+1

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,115598,-115598,0,0,-1,1).

%F G.f.: -x^2*(8*x^6+663*x^5+14968*x^4+26520*x^3+14968*x^2+663*x+8) / ((x-1)*(x^4-340*x^2+1)*(x^4+340*x^2+1)). - _Colin Barker_, Mar 05 2013

%Y Cf. A105839.

%K nonn,easy

%O 1,2

%A _Pierre CAMI_, Apr 06 2005, Apr 22 2005

%E Edited by _N. J. A. Sloane_, Aug 29 2008 at the suggestion of R. J. Mathar

%E More terms (using recursive formula in comment) from _Jon E. Schoenfield_, Jul 10 2010

%E a(18) from _Colin Barker_, Mar 05 2013

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)