[seqfan] Similar sequences A126222 and A166073

Jeremy Gardiner jeremy.gardiner at btinternet.com
Thu Aug 19 12:04:03 CEST 2010


I noticed sequences A126222 and A166073 appear identical with zeros removed:

A126222 Triangle read by rows: T(n,k) is the number of 2-Motzkin paths (i.e.
Motzkin paths with blue and red level steps) without red level steps on the
x-axis, having length n and k level steps (0<=k<=n). (zeros removed)

1, 1, 1, 1, 4, 1, 2, 11, 1, 15, 26, 1, 5, 69, 57, 1, 56, 252, 120, 1, 14,
364, 804, 247, 1, 210, 1800, 2349, 502, 1, 42, 1770, 7515, 6455, 1013, 1,
792, 11055, 27940, 16962,

A166073 Triangle read by rows: a(n,k)=number of permutations in S_n which
avoid the pattern 123 and have exactly k descents. (zeros removed)

1, 1, 1, 1, 4, 1, 2, 11, 1, 15, 26, 1, 5, 69, 57, 1, 56, 252, 120, 1, 14,
364, 804, 247, 1, 210, 1800, 2349, 502, 1, 42, 1770, 7515, 6455, 1013, 1,
792, 11055, 27940, 16962, 2036, 1, 132, 8217






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