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A288111 Number of Dyck paths of semilength n such that each level has exactly four peaks or no peaks. 2
1, 0, 0, 0, 1, 1, 4, 7, 11, 22, 81, 235, 673, 2063, 5716, 13627, 33752, 95729, 298232, 946563, 2977953, 9147328, 27004159, 76880498, 217826819, 637089405, 1949908577, 6160707450, 19627448025, 61909478550, 191681762379, 583025396879, 1756696160636 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
LINKS
EXAMPLE
. a(6) = 4:
. /\/\/\/\
. /\ /\/\/\ /\/\ /\/\ /\/\/\ /\ / \
. / \/ \ / \/ \ / \/ \ / \ .
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, 4$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, 4, 4]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 02 2018, from Maple *)
CROSSREFS
Column k=4 of A288108.
Sequence in context: A104102 A074705 A352216 * A352214 A179165 A369546
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 05 2017
STATUS
approved

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Last modified April 26 04:03 EDT 2024. Contains 371989 sequences. (Running on oeis4.)