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 A201080 Irregular triangle read by rows: number of shifted Schroeder paths of length n and area k. 2
 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 4, 3, 3, 3, 1, 1, 1, 1, 3, 3, 5, 6, 8, 9, 11, 12, 11, 10, 7, 6, 4, 1, 1, 1, 1, 3, 3, 6, 6, 9, 12, 16, 18, 22, 27, 29, 33, 38, 40, 39, 39, 34, 28, 21, 14, 10, 5, 1, 1, 1, 1, 3, 3, 6, 6, 10, 13, 18, 22, 28, 35, 41, 50, 61 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Alois P. Heinz, Rows n = 0..40, flattened Brian Drake, Limits of areas under lattice paths, Discrete Math. 309 (2009), no. 12, 3936-3953. See Example 3. EXAMPLE Triangle begins 1 1 1 1 1 1 2 1 1 1 1 3 3 4 3 3 3 1 1 1 1 3 3 5 6 8 9 11 12 11 10 7 6 4 1 ... MAPLE b:= proc(x, y) option remember; expand(`if`(y>x or y<0, 0, `if`(x=0, 1, b(x-1, y)*z^(2*y)+b(x, y-1)+`if`(y>0, add( b(x-(2*j-1), y-1)*z^((2*y-1)*(2*j-1)), j=1..1+(x-y)/2), 0)))) end: T:= n-> (p-> seq(coeff(p, z, i), i=0..degree(p)))(b(n\$2)): seq(T(n), n=0..8); # Alois P. Heinz, Feb 02 2018 MATHEMATICA b[x_, y_] := b[x, y] = Expand[If[y > x || y < 0, 0, If[x == 0, 1, b[x - 1, y]*z^(2*y) + b[x, y - 1] + If[y > 0, Sum[b[x - (2*j - 1), y - 1]*z^((2*y - 1)*(2*j - 1)), {j, 1, 1 + (x - y)/2}], 0]]]]; T[n_] := Function[p, Table[Coefficient[p, z, i], {i, 0, Exponent[p, z]}]][ b[n, n]]; Table[T[n], {n, 0, 8}] // Flatten (* Jean-François Alcover, Jun 11 2018, after Alois P. Heinz *) CROSSREFS Row sums give A133656. Sequence in context: A258445 A129179 A120621 * A039754 A213919 A337220 Adjacent sequences: A201077 A201078 A201079 * A201081 A201082 A201083 KEYWORD nonn,tabf AUTHOR N. J. A. Sloane, Nov 26 2011 EXTENSIONS More term from Alois P. Heinz, Feb 02 2018 STATUS approved

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Last modified January 31 11:22 EST 2023. Contains 359971 sequences. (Running on oeis4.)