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A114900 Number of compositions of n such that no two adjacent parts are equal, allowing 0. 4
2, 4, 8, 24, 60, 152, 400, 1032, 2656, 6876, 17776, 45912, 118664, 306680, 792480, 2047984, 5292564, 13677160, 35345112, 91340568, 236046088, 610000528, 1576390448, 4073776744, 10527631456, 27205966108, 70306845872, 181690021616, 469531293752, 1213383282936 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

A. Knopfmacher and H. Prodinger, On Carlitz compositions, European Journal of Combinatorics, Vol. 19, No. 5, Jul 1998, pp. 579-589.

FORMULA

G.f.: 2*B(x)/(2-B(x)) where B(x) is g.f. of A003242.

EXAMPLE

The 8 compositions of 2 are 2, 2+0, 1+0+1, 1+0+1+0, 0+2, 0+2+0, 0+1+0+1, 0+1+0+1+0.

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))), j=0..n))

    end:

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

seq(a(n), n=0..30);  # 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]]], {j, 0, n}]]; a[n_] := b[n, -1]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Feb 08 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A003242, A114903.

Sequence in context: A078223 A291405 A231721 * A264570 A115115 A026097

Adjacent sequences:  A114897 A114898 A114899 * A114901 A114902 A114903

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 05 2006

EXTENSIONS

Replaced broken link, Vaclav Kotesovec, May 01 2014

STATUS

approved

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Last modified January 21 19:42 EST 2019. Contains 319350 sequences. (Running on oeis4.)