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A114903 Number of compositions of {1,..,n} such that no two adjacent parts are of equal size (labeled Carlitz compositions), allowing parts to be of size 0. 2
2, 4, 12, 76, 572, 5204, 59340, 782996, 11707324, 197988340, 3720933092, 76811352116, 1730660689580, 42251140165108, 1110607948991028, 31279537587370916, 939737174809843644, 29996522608581396788, 1013814287146517455812, 36168456215193554061044 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

FORMULA

E.g.f.: 2*B(x)/(2-B(x)) where B(x) is e.g.f. of A114902.

a(n) ~ c * d^n * n^(n + 1/2), where d = 0.6907524084725166379194613015033714490019226066943600905783847741049876032..., c = 4.71633079866926561049991146534865892961540468329142429184529629611133729... - Vaclav Kotesovec, Sep 21 2019

MAPLE

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

      `if`(n=0, `if`(i=0, 1, 2), add(`if`(i=j, 0, b(n-j,

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

    end:

a:= n-> b(n, -1):

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

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, If[i == 0, 1, 2], Sum[If[i == j, 0, b[n - j, If[j > n - j, -1, j]]*Binomial[n, j]], {j, 0, n}]]; a[n_] := b[n, -1]; Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Feb 25 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A114900, A114902.

Sequence in context: A085864 A060935 A141522 * A038054 A003180 A002080

Adjacent sequences:  A114900 A114901 A114902 * A114904 A114905 A114906

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 05 2006

STATUS

approved

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Last modified February 21 17:07 EST 2020. Contains 332100 sequences. (Running on oeis4.)