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

1,2

Links

Table of n, a(n) for n=1..19.

Index entries for linear recurrences with constant coefficients, signature (1,254,-254,-1,1).

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

Example

3936 = 254*15 + 111 + 15, 28320 = 254*111 + 111 + 15, 999855 = 254*3936 + 111, 7193295 = 254*28320 + 15.

Mathematica

LinearRecurrence[{1, 254, -254, -1, 1}, {0, 15, 111, 3936, 28320}, 20] (* Harvey P. Dale, Jul 25 2018 *)

Prog

(PARI) for(n=0, 7193295, if(issquare(7*n*(n+1)+1), print1(n, ", ")))

Crossrefs

Sequence in context: A092646 A222117 A105051 * A298123 A370763 A295384

Adjacent sequences: A105037 A105038 A105039 * A105041 A105042 A105043

Keyword

nonn,easy

Author

Gerald McGarvey, Apr 03 2005

Extensions

More terms from Colin Barker, Jun 13 2012

Status

approved