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A288115
Number of Dyck paths of semilength n such that each level has exactly eight peaks or no peaks.
2
1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 29, 71, 148, 302, 596, 1101, 1915, 3485, 8991, 32879, 131942, 595068, 2731434, 11077722, 38438377, 117144042, 324706536, 842734665, 2087025088, 4995608093, 11799404719, 28899101722, 79974175125, 268545121874, 1071998634063
OFFSET
0,11
LINKS
MAPLE
b:= proc(n, k, j) option remember; `if`(n=j, 1, add(
b(n-j, k, i)*(binomial(j-1, i-1)+binomial(i, k)
*binomial(j-1, i-1-k)), i=1..min(j+k, n-j)))
end:
a:= n-> `if`(n=0, 1, b(n, 8$2)):
seq(a(n), n=0..37);
MATHEMATICA
b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[b[n - j, k, i]*(Binomial[j - 1, i - 1] + Binomial[i, k]*Binomial[j - 1, i - 1 - k]), {i, 1, Min[j + k, n - j]}]];
a[n_] := If[n == 0, 1, b[n, 8, 8]];
Table[a[n], {n, 0, 37}] (* Jean-François Alcover, Jun 02 2018, from Maple *)
CROSSREFS
Column k=8 of A288108.
Sequence in context: A093809 A244244 A037157 * A100178 A106113 A362153
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 05 2017
STATUS
approved