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Search: id:A118187
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| A118187 |
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Antidiagonal sums of triangle A118185: a(n) = Sum_{k=0..[n/2]} (4^k)^(n-2*k) for n>=0. |
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+0
3
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| 1, 1, 2, 5, 18, 81, 514, 5185, 73730, 1327361, 33685506, 1359217665, 77311508482, 5567355555841, 565149010231298, 91215553426898945, 20753150033413537794, 5977902509385249259521, 2427296516310194305630210
(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/(1-4^n*x^2). a(2*n) = Sum_{k=0..n} (4^k)^(2(n-k)); a(2*n+1) = Sum_{k=0..n} (4^k)^(2(n-k)+1).
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EXAMPLE
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A(x) = 1/(1-x^2) + x/(1-4x^2) + x^2/(1-16x^2) + x^3/(1-64x^2) +...
= 1 + x + 2*x^2 + 5*x^3 + 18*x^4 + 81*x^5 + 514*x^6 +...
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PROGRAM
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(PARI) a(n)=sum(k=0, n\2, (4^k)^(n-2*k) )
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CROSSREFS
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Cf. A118185 (triangle), A118186 (row sums).
Sequence in context: A006848 A137861 A111916 this_sequence A038720 A089412 A058798
Adjacent sequences: A118184 A118185 A118186 this_sequence A118188 A118189 A118190
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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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