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A114902 Number of compositions of {1,..,n} such that no two adjacent parts are of equal size (labeled Carlitz compositions). 5
1, 1, 1, 7, 21, 81, 793, 4929, 33029, 388537, 3751311, 37585989, 523395777, 6814401361, 90789460427, 1486639926417, 24213653736389, 403184436319401, 7665459211898263, 149067938821523349, 2971265450045056871, 64800464138121854877, 1460876941168812354947 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

FORMULA

a(n) ~ c * d^n * n^(n + 1/2), where d = 0.37565358657373546999489873158654700..., c = 2.0427954030382239202983023897265... - Vaclav Kotesovec, Sep 21 2019

MAPLE

b:= proc(n, i) option remember;

`if`(n=0, 1, add(`if`(i=j, 0, b(n-j,

`if`(j>n-j, 0, j)) *binomial(n, j)), j=1..n))

end:

a:= n-> b(n, 0):

seq(a(n), n=0..25); # Alois P. Heinz, Sep 04 2015

MATHEMATICA

b[n_, i_] := b[n, i] = If[n==0, 1, Sum[If[i==j, 0, b[n-j, If[j>n-j, 0, j]]* Binomial[n, j]], {j, 1, n}]]; a[n_] := b[n, 0]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 20 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A000670, A003242, A007837, A032011.

Column k=1 of A261959.

Sequence in context: A147003 A110683 A092785 * A177369 A164544 A100025

Adjacent sequences: A114899 A114900 A114901 * A114903 A114904 A114905

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 05 2006

STATUS

approved

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Last modified February 7 15:35 EST 2023. Contains 360127 sequences. (Running on oeis4.)