A060569 Consider Pythagorean triples which satisfy X^2+(X+7)^2=Z^2; sequence gives increasing values of Z.

13, 17, 73, 97, 425, 565, 2477, 3293, 14437, 19193, 84145, 111865, 490433, 651997, 2858453, 3800117, 16660285, 22148705, 97103257, 129092113, 565959257, 752403973, 3298652285, 4385331725, 19225954453, 25559586377, 112057074433, 148972186537, 653116492145

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

Sequence in context: A089577 A356079 A214393 * A108265 A069853 A175791

Adjacent sequences: A060566 A060567 A060568 * A060570 A060571 A060572

Keyword

nonn

Author

Sebastiao Antonio da Silva, Apr 12 2001

Extensions

Edited by N. J. A. Sloane, Oct 06 2007

Status

approved