A382168 - OEIS

A382168

Number of triples (i,j,k), 1 <= i < j < k <= n such that A019444(i) < A019444(k) < A019444(j).

0, 0, 1, 1, 1, 7, 7, 17, 17, 17, 38, 38, 38, 74, 74, 119, 119, 119, 185, 185, 263, 263, 263, 368, 368, 368, 504, 504, 657, 657, 657, 847, 847, 847, 1078, 1078, 1331, 1331, 1331, 1631, 1631, 1956, 1956, 1956, 2334, 2334, 2334, 2769, 2769, 3234, 3234, 3234, 3762, 3762, 4323, 4323, 4323, 4953, 4953, 4953, 5656, 5656, 6397, 6397, 6397

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OFFSET

1,6

COMMENTS

Counts occurrences of the pattern 132 in A019444. Note that the Catalan numbers (A000108) count permutations of 1,2,...,n that avoid the pattern 132.

LINKS

Table of n, a(n) for n=1..65.

CROSSREFS

Cf. A000108, A019444, A382162, A382169.

Sequence in context: A198439 A100635 A292084 * A168458 A165138 A196395

Adjacent sequences: A382165 A382166 A382167 * A382169 A382170 A382171

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 31 2025

STATUS

approved