A128768 Number of peak-avoiding compositions with positive parts.

1, 1, 2, 4, 7, 13, 22, 38, 64, 107, 177, 293, 481, 789, 1291, 2110, 3445, 5621, 9167, 14947, 24366, 39716, 64732, 105500, 171941, 280220, 456687, 744280, 1212984, 1976850, 3221762, 5250655, 8557248, 13946172, 22728787, 37042274, 60369723, 98387696, 160347599

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

S. Heubach and T. Mansour, Enumeration of 3-letter patterns in combinations, arXiv:math/0603285 [math.CO], 2006.

Formula

The Heubach/Mansour paper has a complicated g.f.

Maple

b:= proc(n, t, l) option remember; `if`(n=0, 1, add(
      b(n-j, is(j>l), j), j=max(1, `if`(t, l, 1))..n))
    end:
a:= n-> b(n, false, n):
seq(a(n), n=0..40);  # Alois P. Heinz, Oct 24 2017

Mathematica

b[n_, t_, l_] := b[n, t, l] = If[n == 0, 1, Sum[b[n - j, j > l, j], {j, Max[1, If[t, l, 1]], n}]];
a[n_] := b[n, False, n];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Nov 11 2017, after Alois P. Heinz *)
nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(k^2+3*k+1)/Product[(1 - x^j), {j, 1, 2*k + 1}], {k, 0, Sqrt[nmax]}]/(1 + Sum[x^(k*(k + 2))/Product[(1 - x^j), {j, 1, 2*k}], {k, 1, Sqrt[nmax]}])), {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 18 2020 *)

Crossrefs

Cf. A128805.

Sequence in context: A188920 A281362 A319111 * A235607 A254007 A372782

Adjacent sequences: A128765 A128766 A128767 * A128769 A128770 A128771

Keyword

nonn

Author

Ralf Stephan, May 08 2007

Extensions

More terms from Vladeta Jovovic, Oct 04 2007

Status

approved