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Search: id:A093131
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| A093131 |
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Binomial transform of Fib(2n). |
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+0
2
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| 0, 1, 5, 20, 75, 275, 1000, 3625, 13125, 47500, 171875, 621875, 2250000, 8140625, 29453125, 106562500, 385546875, 1394921875, 5046875000, 18259765625, 66064453125, 239023437500, 864794921875, 3128857421875, 11320312500000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Second binomial transform of Fib(n). - Paul Barry (pbarry(AT)wit.ie), Apr 22 2005
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FORMULA
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G.f.: x/(1-5x+5x^2); a(n)=(((5+sqrt(5))/2)^n-((5-sqrt(5))/2)^n)/sqrt(5); a(n)=A093130(n)/2^n.
a(n)=sum{k=0..n, sum{j=0..n, C(n, j)C(j, k)F(j-k)}}; - Paul Barry (pbarry(AT)wit.ie), Feb 15 2005
a(n)=sum{k=0..n, C(n, k)F(n-k)2^k}=sum{k=0..n, C(n, k)F(k)2^(n-k)}; - Paul Barry (pbarry(AT)wit.ie), Apr 22 2005
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CROSSREFS
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Cf. A000045.
Sequence in context: A092490 A094828 A030191 this_sequence A000344 A061278 A000758
Adjacent sequences: A093128 A093129 A093130 this_sequence A093132 A093133 A093134
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 23 2004
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