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A106358
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Number of compositions of n with exactly 2 adjacent equal parts (2 pairs or 1 triple.).
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1
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1, 0, 2, 8, 10, 22, 58, 112, 219, 466, 920, 1787, 3600, 7025, 13532, 26315, 50625, 96775, 185000, 351714, 665942, 1258649, 2371219, 4454004, 8348735, 15612146, 29128863, 54245790, 100828939, 187074952, 346527510, 640878692, 1183480187
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OFFSET
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3,3
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LINKS
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A. Knopfmacher and H. Prodinger, On Carlitz compositions, European Journal of Combinatorics, Vol. 19, 1998, pp. 579-589.
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FORMULA
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a(n) ~ c * d^n * n^2, where d = 1.7502412917183090312497386246... (see A241902), c = 0.0025523594118210599072896951... . - Vaclav Kotesovec, Aug 25 2014
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MAPLE
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b:= proc(n, v) option remember; `if`(n=0, [1, 0$2], add((
p->`if`(i=v, [0, p[1..2][]], p))(b(n-i, i)), i=1..n))
end:
a:= n-> b(n, 0)[3]:
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MATHEMATICA
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b[n_, v_] := b[n, v] = If[n==0, {1, 0, 0}, Sum[If[i==v, Prepend[#[[1;; 2]], 0], #]&[b[n-i, i]], {i, 1, n}]];
a[n_] := b[n, 0][[3]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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