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Search: id:A118674
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| A118674 |
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Sequence allows us to find the solutions of the equation X^2+(X+31)^2=Y^2. |
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12
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| 0, 9, 60, 93, 140, 429, 620, 893, 2576, 3689, 5280, 15089, 21576, 30849, 88020, 125829, 179876, 513093, 733460, 1048469, 2990600, 4274993, 6111000, 17430569, 24916560, 35617593, 101592876, 145224429, 207594620, 592126749, 846430076
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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+31,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)+62 with a(0)=0,a(1)=9,a(2)=60,a(3)=93, a(4)=140, a(5)=429.
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MATHEMATICA
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For the equation: X^2+(X+K)^2=Y^2 with K=2*m^2-1, m>=2 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)=2m+1, a(2)=6*m^2-10m+4, a(3)=3K, a(4)=6*m^2+10m+4, a(5)=40*m^2-58m+21.
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CROSSREFS
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Sequence in context: A039929 A099333 A098327 this_sequence A074431 A081904 A085373
Adjacent sequences: A118671 A118672 A118673 this_sequence A118675 A118676 A118677
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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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