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A128805
Number of valley-avoiding compositions with positive parts.
2
1, 1, 2, 4, 8, 15, 28, 52, 96, 177, 326, 600, 1104, 2032, 3740, 6884, 12672, 23327, 42942, 79052, 145528, 267905, 493192, 907928, 1671424, 3076959, 5664436, 10427772, 19196688, 35339553, 65057260, 119765152, 220477952, 405882064, 747196026, 1375527404
OFFSET
0,3
LINKS
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=1..min(n, `if`(t, l, n))))
end:
a:= n-> b(n, false, 0):
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, 1, Min[n, If[t, l, n]]}]];
a[n_] := b[n, False, 0];
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 + 1)^2)/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. A128768.
Sequence in context: A320452 A073769 A008937 * A141018 A049864 A239554
KEYWORD
nonn
AUTHOR
Ralf Stephan, May 08 2007
EXTENSIONS
More terms from Vladeta Jovovic, Oct 04 2007
STATUS
approved