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 A242352 Number T(n,k) of isoscent sequences of length n with exactly k descents; triangle T(n,k), n>=0, 0<=k<=n+2-ceiling(2*sqrt(n+1)), read by rows. 13
 1, 1, 2, 4, 1, 9, 6, 21, 29, 2, 51, 124, 28, 127, 499, 241, 10, 323, 1933, 1667, 216, 1, 835, 7307, 10142, 2765, 98, 2188, 27166, 56748, 27214, 2637, 22, 5798, 99841, 299485, 227847, 44051, 1546, 2, 15511, 363980, 1514445, 1708700, 563444, 46947, 570 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS An isoscent sequence of length n is an integer sequence [s(1),...,s(n)] with s(1) = 0 and 0 <= s(i) <= 1 plus the number of level steps in [s(1),...,s(i)]. Columns k=0-10 give: A001006, A243474, A243475, A243476, A243477, A243478, A243479, A243480, A243481, A243482, A243483. Row sums give A000110. Last elements of rows give A243484. LINKS Joerg Arndt and Alois P. Heinz, Rows n = 0..114, flattened EXAMPLE T(4,0) = 9: [0,0,0,0], [0,0,0,1], [0,0,0,2], [0,0,0,3], [0,0,1,1], [0,0,1,2], [0,0,2,2], [0,1,1,1], [0,1,1,2]. T(4,1) = 6: [0,0,1,0], [0,0,2,0], [0,0,2,1], [0,1,0,0], [0,1,0,1], [0,1,1,0]. T(5,2) = 2: [0,0,2,1,0], [0,1,0,1,0]. Triangle T(n,k) begins: : 1; : 1; : 2; : 4, 1; : 9, 6; : 21, 29, 2; : 51, 124, 28; : 127, 499, 241, 10; : 323, 1933, 1667, 216, 1; : 835, 7307, 10142, 2765, 98; : 2188, 27166, 56748, 27214, 2637, 22; MAPLE b:= proc(n, i, t) option remember; `if`(n<1, 1, expand(add( `if`(j (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n-1, 0\$2)): seq(T(n), n=0..15); MATHEMATICA b[n_, i_, t_] := b[n, i, t] = If[n<1, 1, Expand[Sum[If[j

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Last modified July 15 14:07 EDT 2024. Contains 374332 sequences. (Running on oeis4.)