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A244714 Number of compositions of n with exactly 2 transitions between different parts. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..1000

EXAMPLE

a(4) = 1: [1,2,1].

a(5) = 4: [1,1,2,1], [1,2,1,1], [1,3,1], [2,1,2].

MAPLE

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);

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, 2];

Table[a[n], {n, 4, 60}] (* Jean-Fran├žois Alcover, Aug 29 2021, after A238279 Maple code *)

CROSSREFS

Column k=2 of A238279.

Sequence in context: A316213 A296985 A338311 * A218212 A305637 A103779

Adjacent sequences:  A244711 A244712 A244713 * A244715 A244716 A244717

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Jul 04 2014

STATUS

approved

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Last modified June 30 03:34 EDT 2022. Contains 354913 sequences. (Running on oeis4.)