A105040 Nonnegative k such that 7*k^2 + 7*k + 1 is a square.
0, 15, 111, 3936, 28320, 999855, 7193295, 253959360, 1827068736, 64504677711, 464068265775, 16383934179360, 117871512438240, 4161454776879855, 29938900091047311, 1056993129393303936, 7604362751613578880, 268472093411122320015, 1931478200009757988335
Offset: 1
Examples
3936 = 254*15 + 111 + 15, 28320 = 254*111 + 111 + 15, 999855 = 254*3936 + 111, 7193295 = 254*28320 + 15.
Links
- Index entries for linear recurrences with constant coefficients, signature (1,254,-254,-1,1).
Programs
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Mathematica
LinearRecurrence[{1,254,-254,-1,1},{0,15,111,3936,28320},20] (* Harvey P. Dale, Jul 25 2018 *) -
PARI
for(n=0,7193295,if(issquare(7*n*(n+1)+1),print1(n,",")))
Formula
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].
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]
a(n) = A253460(n) - 1. - Michel Marcus, Mar 12 2024
Extensions
More terms from Colin Barker, Jun 13 2012