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Search: id:A084637
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| A084637 |
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Binomial transform of (1,0,1,0,1,0,1,1,1,1,1,....). |
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+0
3
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| 1, 1, 2, 4, 8, 16, 32, 65, 136, 293, 642, 1410, 3072, 6606, 14004, 29295, 60592, 124187, 252742, 511672, 1031912, 2075452, 4166408, 8353165, 16732664, 33498977, 67040458, 134134046, 268333872, 536748474, 1073595228, 2147309211
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The sequence starting 1,2,4,... is the binomial transform of (1,1,1,1,1,1,2,2,2...) with a(n)=sum{k=0..5,C(n,k)}+2*sum{k=6..n, C(n,k)}= 2^n-(n^5-5n^4+25n^3+5n^2+94n+120)/120. This gives the partial sums of A084636.
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FORMULA
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a(n)=sum{k=0..2, C(n, 2k)}+sum{k=6..n, C(n, k)}; a(n)=2^n-n(n^4-10n^3+55n^2-110n+184)/120.
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CROSSREFS
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Cf. A084634, A000325, A000225.
Sequence in context: A101333 A023421 A098051 this_sequence A100137 A141366 A049142
Adjacent sequences: A084634 A084635 A084636 this_sequence A084638 A084639 A084640
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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), Jun 06 2003
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