|
Search: id:A113979
|
|
|
| A113979 |
|
Number of compositions of n with an even number of 1's. |
|
+0
2
|
|
| 0, 2, 1, 6, 6, 20, 28, 72, 120, 272, 496, 1056, 2016, 4160, 8128, 16512, 32640, 65792, 130816, 262656, 523776, 1049600, 2096128, 4196352, 8386560, 16781312, 33550336, 67117056, 134209536, 268451840, 536854528, 1073774592, 2147450880
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
More generally, g.f. for number of compositions such that part m occurs with even multiplicity is (1-x)/(1-2*x)*(1-2*x+x^m-x^(m+1))/(1-2*x+2*x^m-2*x^(m+1)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 01 2007
|
|
FORMULA
|
2^(n-2)+2^((n-2)/2) if n is even, else 2^(n-2)-2^((n-3)/2).
G.f.=z(2-3z)/[(1-2z)(1-2z^2)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 03 2006
|
|
EXAMPLE
|
a(4)=6 because the compositions of 4 having an even number of 1's are 4,22,211,121,112, and 1111 (the other compositions of 4 are 31 and 13).
|
|
MAPLE
|
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)
|
|
MATHEMATICA
|
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 *)
|
|
CROSSREFS
|
Cf. A063376, A006516, A063083, A100818, A092295, A111752, A111753, A111723, A111724, A088336, A088506.
Cf. A105422.
Sequence in context: A117753 A062820 A113336 this_sequence A053442 A019082 A052636
Adjacent sequences: A113976 A113977 A113978 this_sequence A113980 A113981 A113982
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 31 2006
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v (rgwv(at)rgwv.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 01 2006
|
|
|
Search completed in 0.002 seconds
|
