|
|
A128768
|
|
Number of peak-avoiding compositions with positive parts.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
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):
|
|
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];
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|