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Search: id:A118182
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| A118182 |
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Antidiagonal sums of triangle A118180: a(n) = Sum_{k=0..[n/2]} (3^k)^(n-2*k) for n>=0. |
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+0
3
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| 1, 1, 2, 4, 11, 37, 164, 1000, 8021, 81001, 1076006, 19683244, 473632031, 14349084877, 571833704648, 31381448626000, 2265367321680041, 205893684435186001, 24615565942378859210, 4052605390737766057684
(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/(1-3^n*x^2). a(2*n) = Sum_{k=0..n} (3^k)^(2(n-k)); a(2*n+1) = Sum_{k=0..n} (3^k)^(2(n-k)+1).
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EXAMPLE
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A(x) = 1/(1-x^2) + x/(1-3x^2) + x^2/(1-9x^2) + x^3/(1-27x^2) +...
= 1 + x + 2*x^2 + 4*x^3 + 11*x^4 + 37*x^5 + 164*x^6 + 1000*x^7 +...
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PROGRAM
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(PARI) a(n)=sum(k=0, n\2, (3^k)^(n-2*k) )
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CROSSREFS
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Cf. A118180 (triangle), A118181 (row sums); A118183, A118184.
Sequence in context: A086611 A035098 A138301 this_sequence A107107 A101898 A065851
Adjacent sequences: A118179 A118180 A118181 this_sequence A118183 A118184 A118185
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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), Apr 15 2006
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