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%I #23 Mar 12 2024 13:00:55
%S 0,15,111,3936,28320,999855,7193295,253959360,1827068736,64504677711,
%T 464068265775,16383934179360,117871512438240,4161454776879855,
%U 29938900091047311,1056993129393303936,7604362751613578880,268472093411122320015,1931478200009757988335
%N Nonnegative k such that 7*k^2 + 7*k + 1 is a square.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,254,-254,-1,1).
%F a(n) = ((7-2*sqrt(7)*(-1)^n)*(8-3*sqrt(7))^((2n-(-1)^n+1)/2)+(7+2*sqrt(7)*(-1)^n)*(8+3*sqrt(7))^((2n-(-1)^n+1)/2)-14)/28. [_Bruno Berselli_, Jun 13 2012].
%F G.f.: -3*x^2*(5*x^2+32*x+5)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)). [_Colin Barker_, Jul 22 2012]
%F a(n) = A253460(n) - 1. - _Michel Marcus_, Mar 12 2024
%e 3936 = 254*15 + 111 + 15, 28320 = 254*111 + 111 + 15, 999855 = 254*3936 + 111, 7193295 = 254*28320 + 15.
%t LinearRecurrence[{1,254,-254,-1,1},{0,15,111,3936,28320},20] (* _Harvey P. Dale_, Jul 25 2018 *)
%o (PARI) for(n=0,7193295,if(issquare(7*n*(n+1)+1),print1(n,",")))
%K nonn,easy
%O 1,2
%A _Gerald McGarvey_, Apr 03 2005
%E More terms from _Colin Barker_, Jun 13 2012