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Search: id:A111766
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| A111766 |
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Numbers occurring in three Pythagorean triples of the form: odd: a, (a^2-1)/2, (a^2+1)/2 OR even: a, a^2/4-1, a^2/4+1. |
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+0
1
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OFFSET
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1,1
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COMMENT
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This parallels Cassini's identity for Fibonacci numbers (Mathworld)
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FORMULA
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a(n) = P(n-1)*P(n+1) = Pn^2 + (-1)^n where P is the first Pell series (a1=1, a2=2)
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EXAMPLE
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e.g. a(5) = P(4)*P(6) = 12*70 = 840 = P(5)-1 = 29^2-1
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CROSSREFS
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Sequence in context: A009411 A080996 A020055 this_sequence A009424 A009601 A009676
Adjacent sequences: A111763 A111764 A111765 this_sequence A111767 A111768 A111769
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KEYWORD
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nonn
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AUTHOR
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Jeremy C. Buchanan (jbuchanan(AT)myhww.org), Nov 21 2005
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