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A244715
Number of compositions of n with exactly 3 transitions between different parts.
2
2, 10, 36, 86, 200, 374, 680, 1122, 1796, 2694, 3954, 5600, 7752, 10448, 13798, 18072, 23032, 29218, 36390, 45044, 54870, 66852, 79790, 95550, 112662, 132938, 154752, 180614, 207764, 239784, 273898, 312922, 354240, 401826, 451598, 508134, 567756, 634634, 705506
OFFSET
6,1
LINKS
MAPLE
b:= proc(n, v) option remember; `if`(n=0, [1, 0$3],
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..3][]]), i=1..n))
end:
a:= n-> b(n, 0)[4]:
seq(a(n), n=6..60);
MATHEMATICA
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, 3];
Table[a[n], {n, 6, 60}] (* Jean-François Alcover, Aug 29 2021, after A238279 Maple code *)
CROSSREFS
Column k=3 of A238279.
Sequence in context: A309889 A155894 A317454 * A212573 A100535 A340885
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jul 04 2014
STATUS
approved