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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 (list; graph; refs; listen; history; text; internal format)
 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. Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets 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 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 Adjacent sequences: A128802 A128803 A128804 * A128806 A128807 A128808 KEYWORD nonn AUTHOR Ralf Stephan, May 08 2007 EXTENSIONS More terms from Vladeta Jovovic, Oct 04 2007 STATUS approved

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Last modified May 30 07:21 EDT 2023. Contains 363045 sequences. (Running on oeis4.)