OFFSET
1,1
COMMENTS
The sequence gives the values of Z in X^2 + Y^2 = Z^2 where Y = X + 7 and gcd(X,Y,Z)=1. The values of X are given by the formula: X(1)=5, X(2)=8, X(3)=48, X(4)=65, X(n) = 6*X(n-2) - X(n-4) + 14 for n >= 5 - see A117474. Also, Y - X = 7, which is the second term in A058529. We have Z(1)=13, Z(2)=17, Z(3)=73, Z(4)=97, Z(n)=6*Z(n-2) - Z(n-4) for n >= 5. - Andras Erszegi (erszegi.andras(AT)chello.hu), Mar 19 2006
LINKS
Robert Israel, Table of n, a(n) for n = 1..2608
Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1).
FORMULA
G.f.: (13 + 17 x - 5 x^2 - 5 x^3)/(1 - 6 x^2 + x^4). - Robert Israel, Jul 17 2017
MAPLE
f:=proc(n) option remember; if n=1 then RETURN(13) fi; if n=2 then RETURN(17) fi; if n=3 then RETURN(73) fi; if n=4 then RETURN(97) fi; 6*f(n-2)-f(n-4); end;
MATHEMATICA
LinearRecurrence[{0, 6, 0, -1}, {13, 17, 73, 97}, 30] (* Harvey P. Dale, Dec 02 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Sebastiao Antonio da Silva, Apr 12 2001
EXTENSIONS
Edited by N. J. A. Sloane, Oct 06 2007
STATUS
approved