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Search: id:A118337
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| A118337 |
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Sequence allows us to find the solutions of the equation X^2+(X+23)^2=Y^2. |
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1
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| 0, 12, 33, 69, 133, 252, 460, 832, 1525, 2737, 4905, 8944, 16008, 28644, 52185, 93357, 167005, 304212, 544180, 973432, 1773133, 3171769, 5673633, 10334632, 18486480, 33068412, 60234705, 107747157, 192736885, 351073644, 627996508, 1123352944
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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+23,Y) ordered by increasing Y; sequence gives X values.
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REFERENCES
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Mohamed Bouhamida(Algeria),E.Mail:bhmd95(AT)yahoo.fr
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FORMULA
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a(n)=6*a(n-3)-a(n-6)+46 with a(0)=0,a(1)=12,a(2)=33,a(3)=69,a(4)=133,a(5)=252.
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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 is an odd number, p>=5 and K is not a power of a natural integer, 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. E.g.: K=23, 47, 79, 119, 167, 223, ... If K=223 than p=15.
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CROSSREFS
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Cf. A118120, A118554, A118611, A118630, A011379, A045991.
Sequence in context: A063296 A051624 A039338 this_sequence A032604 A043161 A043941
Adjacent sequences: A118334 A118335 A118336 this_sequence A118338 A118339 A118340
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KEYWORD
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nonn,uned
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AUTHOR
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Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 14 2006
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