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A076295
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Consider all Pythagorean triples (Y-7,Y,Z); sequence gives Y values.
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4
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4, 7, 12, 15, 28, 55, 72, 147, 304, 403, 840, 1755, 2332, 4879, 10212, 13575, 28420, 59503, 79104, 165627, 346792, 461035, 965328, 2021235, 2687092, 5626327, 11780604, 15661503, 32792620
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| First two terms included for consistency with A076293.
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n) =6a(n-3)-a(n-6)-14 =(A076293(n)+7)/2 =sqrt(A076294(n)^2-A076296(n)^2) =A076296(n)+7. a(3n+1)=7*A046090(n).
a(0)=4, a(1)=7, a(2)=12, a(3)=15, a(4)=28, a(5)=55, a(6)=72, a(n)= a(n-1)+ 6*a(n-3)-6*a(n-4)-a(n-6)+a (n-7) [From Harvey P. Dale, Feb 02 2012]
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EXAMPLE
| 15 is in the sequence as the longer leg of the (8,15,17) triangle.
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MATHEMATICA
| LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {4, 7, 12, 15, 28, 55, 72}, 40] (* From Harvey P. Dale, Feb 02 2012 *)
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CROSSREFS
| Cf. A046090, A076293, A076294, A076296.
Sequence in context: A134659 A075624 A008333 * A083030 A005005 A190460
Adjacent sequences: A076292 A076293 A076294 * A076296 A076297 A076298
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KEYWORD
| nonn,changed
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Oct 05 2002
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