The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 15 22:50 EDT 2024. Contains 373412 sequences. (Running on oeis4.)