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A244714
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Number of compositions of n with exactly 2 transitions between different parts.
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2
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1, 4, 14, 29, 56, 100, 148, 230, 322, 446, 573, 778, 953, 1215, 1456, 1806, 2134, 2542, 2944, 3477, 3968, 4600, 5186, 5872, 6657, 7446, 8304, 9217, 10258, 11172, 12465, 13564, 14867, 16072, 17716, 18816, 20832, 22055, 24144, 25504, 27904, 29168, 32051, 33375
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OFFSET
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4,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 4..1000
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EXAMPLE
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a(4) = 1: [1,2,1].
a(5) = 4: [1,1,2,1], [1,2,1,1], [1,3,1], [2,1,2].
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MAPLE
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b:= proc(n, v) option remember; `if`(n=0, [1, 0$2],
add(`if`(v in [0, i], b(n-i, `if`(i<=n-i, i, -1)),
[0, b(n-i, `if`(i<=n-i, i, -1))[1..2][]]), i=1..n))
end:
a:= n-> b(n, 0)[3]:
seq(a(n), n=4..60);
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MATHEMATICA
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b[n_, v_] := b[n, v] = If[n == 0, 1, Expand[Sum[b[n - i, i]*
If[v == 0 || v == i, 1, x], {i, n}]]];
a[n_] := Coefficient[b[n, 0], x, 2];
Table[a[n], {n, 4, 60}] (* Jean-François Alcover, Aug 29 2021, after A238279 Maple code *)
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CROSSREFS
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Column k=2 of A238279.
Sequence in context: A316213 A296985 A338311 * A218212 A305637 A103779
Adjacent sequences: A244711 A244712 A244713 * A244715 A244716 A244717
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KEYWORD
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nonn
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AUTHOR
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Joerg Arndt and Alois P. Heinz, Jul 04 2014
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STATUS
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approved
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