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Search: id:A129836
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| A129836 |
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Sequence allows us to find the solutions of the equation: X^2+(X+97)^2=Y^2. |
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11
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| 0, 15, 228, 291, 368, 1575, 1940, 2387, 9416, 11543, 14148, 55115, 67512, 82695, 321468, 393723, 482216, 1873887, 2295020, 2810795, 10922048, 13376591, 16382748, 63658595, 77964720, 95485887, 371029716
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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+97,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)+194 with a(0)=0,a(1)=15,a(2)=228,a(3)=291, a(4)=368,a(5)=1575.
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MAPLE
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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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Cf. A118673, A118674.
Adjacent sequences: A129833 A129834 A129835 this_sequence A129837 A129838 A129839
Sequence in context: A012643 A067222 A041422 this_sequence A075262 A097185 A097582
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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 21 2007
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