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A114900
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Number of compositions of n such that no two adjacent parts are equal, allowing 0.
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4
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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
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OFFSET
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0,1
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LINKS
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A. Knopfmacher and H. Prodinger, On Carlitz compositions, European Journal of Combinatorics, Vol. 19, No. 5, Jul 1998, pp. 579-589.
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FORMULA
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G.f.: 2*B(x)/(2-B(x)) where B(x) is g.f. of A003242.
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EXAMPLE
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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.
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MAPLE
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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):
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MATHEMATICA
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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-François Alcover, Feb 08 2017, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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