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Search: id:A118675
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| A118675 |
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Sequence allows us to find the solutions of the equation X^2+(X+47)^2=Y^2. |
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+0
7
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| 0, 16, 85, 141, 225, 616, 940, 1428, 3705, 5593, 8437, 21708, 32712, 49288, 126637, 190773, 287385, 738208, 1112020, 1675116, 4302705, 6481441, 9763405, 25078116, 37776720, 56905408, 146166085, 220178973, 331669137, 851918488, 1283297212
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OFFSET
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0,2
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COMMENT
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Consider all Pythagorean triples (X,X+47,Y) ordered by increasing Y; sequence gives X values.
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FORMULA
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a(n)=6*a(n-3)-a(n-6)+94 with a(0)=0,a(1)=16,a(2)=85,a(3)=141, a(4)=225, a(5)=616.
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MATHEMATICA
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For the equation X^2+(X+K)^2 = Y^2 with K = p^2-2, p> = 5 and K is a prime number, the X values are given by the sequence defined by: a(n) = 6*a(n-3)-a(n-6)+2K with a(0) = 0, a(1) = 2p+2, a(2) = 3*p^2-10p+8, a(3) = 3K, a(4) = 3*p^2+10p+8, a(5) = 20*p^2-58p+42.
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CROSSREFS
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Adjacent sequences: A118672 A118673 A118674 this_sequence A118676 A118677 A118678
Sequence in context: A056571 A053909 A030693 this_sequence A070052 A022676 A035291
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KEYWORD
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nonn
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AUTHOR
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Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 19 2006
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