The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A114691 Triangle read by rows: T(n,k) is the number of hill-free Schroeder paths of length 2n that have k weak ascents (1<=k<=n-1 for n>=2; k=1 for n=1). A Schroeder path of length 2n is a lattice path from (0,0) to (2n,0) consisting of U=(1,1), D=(1,-1) and H=(2,0) steps and never going below the x-axis. A hill is a peak at height 1. A weak ascent in a Schroeder path is a maximal sequence of consecutive U and H steps. 0
 1, 3, 7, 4, 15, 26, 4, 31, 108, 54, 4, 63, 366, 380, 90, 4, 127, 1104, 1950, 960, 134, 4, 255, 3090, 8284, 6966, 2008, 186, 4, 511, 8212, 31030, 39780, 19550, 3716, 246, 4, 1023, 21014, 106252, 192802, 144472, 46670, 6308, 314, 4, 2047, 52248, 340190 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row n contains n-1 terms (n>=2). Row sums are the little Schroeder numbers (A001003). LINKS Table of n, a(n) for n=1..49. FORMULA G.f.=G=z(t+H)/(1-z-zH), where H is given by H =z(2+H)(t+H). EXAMPLE T(3,2)=4 because we have (UH)D(H),(UU)DD(H),(UU)D(H)D and (UU)D(U)DD, where U=(1,1), D=(1,-1) and H=(2,0) (the weak ascents are shown between parentheses). Triangle starts: 1; 3; 7,4; 15,26,4; 31,108,54,4; MAPLE H:=(1-z*t-2*z-sqrt(1-2*z*t-4*z+z^2*t^2-4*z^2*t+4*z^2))/2/z: G:=z*(t+H)/(1-z-z*H): Gser:=simplify(series(G, z=0, 15)): for n from 1 to 11 do P[n]:=coeff(Gser, z^n) od: 1; for n from 2 to 11 do seq(coeff(P[n], t^j), j=1..n-1) od; # yields sequence in triangular form CROSSREFS Cf. A114655. Sequence in context: A218616 A323173 A324184 * A023639 A291534 A331733 Adjacent sequences: A114688 A114689 A114690 * A114692 A114693 A114694 KEYWORD nonn,tabf AUTHOR Emeric Deutsch, Dec 24 2005 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 6 20:05 EDT 2023. Contains 363151 sequences. (Running on oeis4.)