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A123685 Counts compositions as described by table A047969; however, only those ending with an odd part are considered. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 A189916

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

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Last modified June 19 13:26 EDT 2019. Contains 324222 sequences. (Running on oeis4.)