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Search: id:A117403
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| A117403 |
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Antidiagonal sums of triangle A117401: a(n) = Sum_{k=0..[n/2]} 2^((n-2*k)*k) for n>=0. |
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+0
3
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| 1, 1, 2, 3, 6, 13, 34, 105, 386, 1681, 8706, 53793, 395266, 3442753, 35659778, 440672385, 6476038146, 112812130561, 2336999211010, 57759810847233, 1697654543745026, 59146046307566593, 2450521284684021762
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: A(x) = Sum_{n>=0} x^n/(1-2^n*x^2). a(2*n) = Sum_{k=0..n} 4^((n-k)*k); a(2*n+1) = Sum_{k=0..n} 2^k*4^((n-k)*k).
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EXAMPLE
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A(x) = 1/(1-x^2) + x/(1-2x^2) + x^2/(1-4x^2) + x^3/(1-8x^2) + ...
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PROGRAM
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(PARI) a(n)=sum(k=0, n\2, 2^((n-2*k)*k))
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CROSSREFS
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Cf. A117401 (triangle), A117402 (row sums).
Sequence in context: A005554 A077212 A076836 this_sequence A002877 A065845 A137273
Adjacent sequences: A117400 A117401 A117402 this_sequence A117404 A117405 A117406
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 12 2006
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