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A060569 Consider Pythagorean triples which satisfy X^2+(X+7)^2=Z^2; sequence gives increasing values of Z. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A076789 A089577 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

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Last modified September 16 06:38 EDT 2019. Contains 327090 sequences. (Running on oeis4.)