A117474 The values of 'a' in a^2 + b^2 = c^2 where b - a = 7 and gcd(a,b,c)=1.

5, 8, 48, 65, 297, 396, 1748, 2325, 10205, 13568, 59496, 79097, 346785, 461028, 2021228, 2687085, 11780597, 15661496, 68662368, 91281905, 400193625, 532029948, 2332499396, 3100897797, 13594802765, 18073356848

Offset: 1

Author

Andras Erszegi (erszegi.andras(AT)chello.hu), Mar 19 2006

Keywords

• nonn
• easy

Comments

The values of 'c' are in A060569.

Examples

			a(5) = 6*48 - 5 + 14 = 297, 297^2 + 304^2 = 425^2, 304 - 297 = 7, and gcd(297, 304, 425) = 1.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-1,1).

Crossrefs

Cf. A060569.

Programs

Maple

g:=proc(n) option remember; if n=1 then RETURN(5) fi; if n=2 then RETURN(8) fi; if n=3 then RETURN(48) fi; if n=4 then RETURN(65) fi; 6*g(n-2)-g(n-4)+14; end; # N. J. A. Sloane, Oct 06 2007

Mathematica

LinearRecurrence[{1,6,-6,-1,1},{5,8,48,65,297},40] (* Harvey P. Dale, May 07 2025 *)

Formula

a(n) = 6*a(n-2) - a(n-4) + 14; a(1)=5, a(2)=8, a(3)=48, a(4)=65.

G.f.: x*(3*x^4 + x^3 - 10*x^2 - 3*x-5) / ((x-1)*(x^2-2*x-1)*(x^2+2*x-1)). [Colin Barker, Dec 17 2012]