A123685 Counts compositions as described by table A047969; however, only those ending with an odd part are considered.

1, 1, 0, 1, 1, 1, 1, 3, 4, 0, 1, 7, 14, 2, 1, 1, 15, 46, 14, 7, 0, 1, 31, 146, 74, 43, 3, 1, 1, 63, 454, 350, 247, 33, 10, 0, 1, 127, 1394, 1562, 1363, 273, 88, 4, 1, 1, 255, 4246, 6734, 7327, 2013, 724, 60, 13, 0, 1, 511, 12866, 28394, 38683, 13953, 5716, 676, 149, 5, 1, 1

Offset

1,8

Links

Alois P. Heinz, Antidiagonals n = 1..141, flattened

Example

Row four of table A047969 counts the 14 compositions
4
31 13 32 23 33
211 121 112 221 212 122 222
1111
whereas A123685 only counts
31 13 32 33
121 112 122
and 1111

Maple

g:= proc(b, t, l, m) option remember; `if`(t=0, b*l, add(
      g(b, t-1, irem(k, 2), m), k=1..m-1)+g(1, t-1, irem(m, 2), m))
    end:
A:= (n, k)-> g(0, k, 0, n):
seq(seq(A(n, d+1-n), n=1..d), d=1..13); # Alois P. Heinz, Nov 06 2009

Mathematica

g[b_, t_, l_, m_] := g[b, t, l, m] = If[t == 0, b*l, Sum[g[b, t-1, Mod[k, 2], m], {k, 1, m-1}] + g[1, t-1, Mod[m, 2], m]]; A[n_, k_] := g[0, k, 0, n]; Table [Table [A[n, d+1-n], {n, 1, d}], {d, 1, 13}] // Flatten (* Jean-François Alcover, Feb 20 2015, after Alois P. Heinz *)

Crossrefs

Diagonals include A000012, A059841, A000225, A123684 and A027649.

Sequence in context: A175646 A324362 A073234 * A124917 A228550 A354520

Adjacent sequences: A123682 A123683 A123684 * A123686 A123687 A123688

Keyword

nonn,tabl

Author

Alford Arnold, Oct 11 2006

Extensions

More terms from Alois P. Heinz, Nov 06 2009

Status

approved