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Search: id:A084638
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| A084638 |
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Binomial transform of (1,0,1,0,1,0,1,0,2,0,2,0,2,....). |
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1
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| 1, 1, 2, 4, 8, 16, 32, 64, 129, 265, 558, 1200, 2610, 5682, 12288, 26292, 55587, 116179, 240366, 493108, 1004780, 2036692, 4112144, 8278552, 16631717, 33364381, 66863358, 133903816, 268037862, 536371734, 1073120208, 2146715436
(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 (1,1,1,1,1,1,1,2,2...) with a(n)=sum{k=0..6,C(n,k)}+2*sum{k=7..n, C(n,k)}=2^(n+1)-A008859(n). This gives the partial sums of A084637.
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FORMULA
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a(n)=sum{k=0..3, C(n, 2k)}+2*sum{k=4..floor(n/2), C(n, 2k)}; a(n)=(n^6-15n^5+115n^4-405n^3+964n^2-660n+720)/720+2*sum{k=4..floor(n/2), C(n, 2k)}.
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CROSSREFS
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Cf. A084634, A084635, A084636, A000325, A000225.
Sequence in context: A079845 A117302 A023422 this_sequence A006211 A101333 A023421
Adjacent sequences: A084635 A084636 A084637 this_sequence A084639 A084640 A084641
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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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