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Search: id:A113980
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| A113980 |
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Number of compositions of n with an odd number of 1's. |
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+0
1
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| 1, 0, 3, 2, 10, 12, 36, 56, 136, 240, 528, 992, 2080, 4032, 8256, 16256, 32896, 65280, 131328, 261632, 524800, 1047552, 2098176, 4192256, 8390656, 16773120, 33558528, 67100672, 134225920, 268419072, 536887296, 1073709056, 2147516416
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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2^(n-2)-2^((n-2)/2) if n is even, else 2^(n-2)+2^((n-3)/2).
G.f.=z(1-z)^2/[(1-2z)(1-2z^2)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 03 2006
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EXAMPLE
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a(4)=2 because only the compositions 31 and 13 of 4 have an odd number of 1's (the other compositions are 4,22,211,121,112, and 1111).
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MAPLE
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a:=proc(n) if n mod 2 = 0 then 2^(n-2)-2^((n-2)/2) else 2^(n-2)+2^((n-3)/2) fi end: seq(a(n), n=1..38); (Deutsch)
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MATHEMATICA
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f[n_] := If[EvenQ[n], 2^(n - 2) - 2^((n - 2)/2), 2^(n - 2) + 2^((n - 3)/2)]; Array[f, 34] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A020522, A007582, A063083, A100818, A092295, A111752, A111753, A111723, A111724, A088336, A088506.
Cf. A105422.
Adjacent sequences: A113977 A113978 A113979 this_sequence A113981 A113982 A113983
Sequence in context: A103245 A019242 A064367 this_sequence A095675 A006743 A091811
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 31 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 01 2006
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