Sebastiao Antonio da Silva - cp's OEIS frontend

User: Sebastiao Antonio da Silva

Sebastiao Antonio da Silva has authored 1 sequences.

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

Sebastiao Antonio da Silva, Apr 12 2001

nonn

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

Robert Israel, Table of n, a(n) for n = 1..2608
Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1).

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;

LinearRecurrence[{0,6,0,-1},{13,17,73,97},30] (* Harvey P. Dale, Dec 02 2017 *)

G.f.: (13 + 17 x - 5 x^2 - 5 x^3)/(1 - 6 x^2 + x^4). - Robert Israel, Jul 17 2017

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

cp's OEIS Frontend

User: Sebastiao Antonio da Silva

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

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