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 A199915 Triangle read by rows: T(n,k) is the number of n-step paths from (0,0) to (0,k) that stay in the first quadrant (but may touch the axes) consisting of steps (1,0), (0,1), (0,-1) and (-1,1). 5
 1, 0, 1, 1, 1, 1, 1, 2, 3, 1, 2, 7, 5, 6, 1, 7, 10, 21, 14, 10, 1, 10, 38, 48, 51, 35, 15, 1, 38, 89, 135, 168, 120, 76, 21, 1, 89, 229, 441, 458, 474, 281, 147, 28, 1, 229, 752, 1121, 1604, 1475, 1188, 637, 260, 36, 1, 752, 1873, 3692, 4772, 5100, 4329, 2800, 1366, 429, 45, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Alois P. Heinz, Rows n = 0..140, flattened EXAMPLE T(4,2) = 5: ((1,0),(1,0),(-1,1),(-1,1)); ((1,0),(-1,1),(1,0),(-1,1)); ((0,1),(0,1),(0,1),(0,-1)); ((0,1),(0,1),(0,-1),(0,1)); ((0,1),(0,-1),(0,1),(0,1)). Triangle begins: 1; 0, 1; 1, 1, 1; 1, 2, 3, 1; 2, 7, 5, 6, 1; 7, 10, 21, 14, 10, 1; 10, 38, 48, 51, 35, 15, 1; MAPLE b:= proc(n, k, x, y) option remember; `if`(n<0 or x<0 or y<0 or n b(n, k, 0, 0): seq(seq(T(n, k), k=0..n), n=0..12); MATHEMATICA b[n_, k_, x_, y_] := b[n, k, x, y] = If[n<0 || x<0 || y<0 || n

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Last modified December 3 22:01 EST 2023. Contains 367540 sequences. (Running on oeis4.)