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 A242351 Number T(n,k) of isoscent sequences of length n with exactly k ascents; triangle T(n,k), n>=0, 0<=k<=n+3-ceiling(2*sqrt(n+2)), read by rows. 12
 1, 1, 1, 1, 1, 4, 1, 11, 3, 1, 26, 25, 1, 57, 128, 17, 1, 120, 525, 229, 2, 1, 247, 1901, 1819, 172, 1, 502, 6371, 11172, 3048, 53, 1, 1013, 20291, 58847, 33065, 2751, 7, 1, 2036, 62407, 280158, 275641, 56905, 1422, 1, 4083, 187272, 1242859, 1945529, 771451, 61966, 436 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 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: A000012, A000295, A243228, A243229, A243230, A243231, A243232, A243233, A243234, A243235, A243236. Row sums give A000110. Last elements of rows give A243237. LINKS Joerg Arndt and Alois P. Heinz, Rows n = 0..100, flattened EXAMPLE T(4,0) = 1: [0,0,0,0]. T(4,1) = 11: [0,0,0,1], [0,0,0,2], [0,0,0,3], [0,0,1,0], [0,0,1,1], [0,0,2,0], [0,0,2,1], [0,0,2,2], [0,1,0,0], [0,1,1,0], [0,1,1,1]. T(4,2) = 3: [0,0,1,2], [0,1,0,1], [0,1,1,2]. Triangle T(n,k) begins:   1;   1;   1,    1;   1,    4;   1,   11,     3;   1,   26,    25;   1,   57,   128,    17;   1,  120,   525,   229,     2;   1,  247,  1901,  1819,   172;   1,  502,  6371, 11172,  3048,   53;   1, 1013, 20291, 58847, 33065, 2751, 7;   ... MAPLE b:= proc(n, i, t) option remember; `if`(n<1, 1, expand(add(       `if`(j>i, x, 1) *b(n-1, j, t+`if`(j=i, 1, 0)), j=0..t+1)))     end: T:= n-> (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>i, x, 1]*b[n-1, j, t + If[j == i, 1, 0]], {j, 0, t+1}]]]; T[n_] := Function[{p}, Table[ Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][b[n-1, 0, 0]]; Table[T[n], {n, 0, 15}] // Flatten (* Jean-François Alcover, Feb 09 2015, after Maple *) CROSSREFS Cf. A048993 (for counting level steps), A242352 (for counting descents), A137251 (ascent sequences counting ascents), A238858 (ascent sequences counting descents), A242153 (ascent sequences counting level steps), A083479. Sequence in context: A091156 A092288 A111964 * A124324 A178519 A094503 Adjacent sequences:  A242348 A242349 A242350 * A242352 A242353 A242354 KEYWORD nonn,tabf AUTHOR Joerg Arndt and Alois P. Heinz, May 11 2014 STATUS approved

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Last modified June 16 04:54 EDT 2019. Contains 324145 sequences. (Running on oeis4.)