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A261665 Triangle read by rows: T(n,k) = number of k-classes of permutations of n letters avoiding the pattern 132 (n>=1, 0 <= k <= n-1). 1
1, 2, 2, 4, 5, 5, 9, 12, 14, 14, 21, 30, 37, 42, 42, 51, 76, 99, 118, 132, 132, 127, 196, 265, 331, 387, 429, 429, 323, 512, 714, 922, 1124, 1298, 1430, 1430, 835, 1353, 1934, 2568, 3227, 3872, 4433, 4862, 4862, 2188, 3610, 5268, 7156, 9225, 11384, 13507, 15366, 16796, 16796 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
See Baril et al. (2014) for precise definition.
Interpolates between Motzkin numbers (A001006) and Catalan numbers (A000108).
LINKS
J.-L. Baril, T. Mansour, A. Petrossian, Equivalence classes of permutations modulo excedances, Journal of Combinatorics, Volume 5 (2014), Number 4, doi:10.4310/JOC.2014.v5.n4.a4. See Table 2.
FORMULA
The proof of Theorem 3.1 in Baril et al. (2014) gives a recurrence for the numbers T(n,k).
EXAMPLE
1
2 2
4 5 5
9 12 14 14
21 30 37 42 42
51 76 99 118 132 132
127 196 265 331 387 429 429
323 512 714 922 1124 1298 1430 1430
835 1353 1934 2568 3227 3872 4433 4862 4862
2188 3610 5268 7156 9225 11384 13507 15366 16796 16796
MAPLE
A261665 := proc(n, k)
option remember;
if n = k then
A000108(n);
elif k < 0 or n <=k then
0 ;
else
procname(n-1, k+1)+add(procname(n-1-i, k-i)*A000108(i), i=0..k) ;
end if;
end proc: # R. J. Mathar, Sep 07 2015
MATHEMATICA
T[n_, k_] := T[n, k] = If[n == k, CatalanNumber[n], If[k < 0 || n <= k, 0, T[n-1, k+1] + Sum[T[n-1-i, k-i] CatalanNumber[i], {i, 0, k}]]];
Table[T[n, k], {n, 1, 10}, {k, 0, n-1}] // Flatten (* Jean-François Alcover, Apr 07 2020 *)
CROSSREFS
Sequence in context: A325260 A325325 A240851 * A208096 A049269 A085085
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Sep 01 2015
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)