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A288113 Number of Dyck paths of semilength n such that each level has exactly six peaks or no peaks. 2
1, 0, 0, 0, 0, 0, 1, 1, 6, 16, 31, 56, 102, 179, 426, 1490, 5164, 18715, 73281, 253183, 741420, 1915072, 4599352, 10845192, 26990806, 76446936, 251549461, 918616924, 3497341145, 13161267180, 47114251055, 157204766841, 487208649994, 1416324380706, 3944267803650 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,9
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, 6$2)):
seq(a(n), n=0..40);
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, 6, 6]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 02 2018, from Maple *)
CROSSREFS
Column k=6 of A288108.
Sequence in context: A244242 A092286 A301723 * A276917 A097118 A369548
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 05 2017
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)