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A261962
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Number of compositions of n such that no part equals any of its two immediate predecessors.
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9
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1, 1, 1, 3, 3, 5, 11, 15, 23, 37, 67, 101, 165, 265, 419, 691, 1123, 1789, 2909, 4657, 7515, 12183, 19657, 31635, 51101, 82449, 132989, 214623, 346485, 558587, 901399, 1454949, 2347157, 3787197, 6111131, 9858931, 15908393, 25669125, 41416849, 66826277
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) ~ c * d^n, where d = 1.61350953985228953675390530863679475666564394885974..., c = 0.5270561325668460003703909484716134447490733801644227... - Vaclav Kotesovec, Sep 21 2019
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MAPLE
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b:= proc(n, i, j) option remember; `if`(n=0, 1, add(
`if`(k=i or k=j, 0, (t-> b(t, `if`(k>t, 0, k),
`if`(i>t, 0, i)))(n-k)), k=1..n))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..50);
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MATHEMATICA
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b[n_, i_, j_] := b[n, i, j] = If[n == 0, 1, Sum[If[k == i || k == j, 0, Function[t, b[t, If[k>t, 0, k], If[i>t, 0, i]]][n - k]], {k, 1, n}]];
a[n_] := b[n, 0, 0];
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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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