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

Offset: 1

Author

N. J. A. Sloane, Mar 31 2025

Keywords

• nonn

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.

Crossrefs

Cf. A000108, A019444, A382162, A382169.