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Search: id:A114706
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| A114706 |
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Triangle read by rows: T(n,k) is the number of hill-free Schroeder paths of length 2n and having k ascents (n>=1; 0<=k<=n-1). A Schroeder path of length 2n is a lattice path from (0,0) to (2n,0) consisting of U=(1,1), D=(1,-1) and H=(2,0) steps and never going below the x-axis. A hill is a peak at height 1. An ascent in a Schroeder path is a maximal sequence of consecutive U steps. |
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| 1, 1, 2, 1, 8, 2, 1, 22, 20, 2, 1, 52, 106, 36, 2, 1, 114, 420, 310, 56, 2, 1, 240, 1410, 1840, 706, 80, 2, 1, 494, 4260, 8714, 5832, 1382, 108, 2, 1, 1004, 11978, 35484, 36898, 15100, 2442, 140, 2, 1, 2026, 31988, 129758, 194216, 122674, 34012, 4006, 176, 2, 1
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