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!)
 A121484 Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having k peaks at even level (n>=1,0<=k<=n-1). A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing. 3
 1, 1, 1, 2, 2, 1, 4, 6, 2, 1, 8, 13, 10, 2, 1, 16, 34, 23, 13, 2, 1, 33, 74, 75, 32, 16, 2, 1, 66, 178, 180, 124, 40, 19, 2, 1, 136, 390, 497, 321, 180, 48, 22, 2, 1, 274, 895, 1192, 1004, 488, 244, 56, 25, 2, 1, 562, 1958, 3033, 2598, 1701, 682, 317, 64, 28, 2, 1, 1138, 4374 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Row sums are the odd-subscripted Fibonacci numbers (A001519). T(n,0)=A121485(n). Sum(k*T(n,k),k=0..n-1)=A121486(n). LINKS Table of n, a(n) for n=1..68. E. Barcucci, A. Del Lungo, S. Fezzi and R. Pinzani, Nondecreasing Dyck paths and q-Fibonacci numbers, Discrete Math., 170, 1997, 211-217. FORMULA G.f.: G(t,z) = z(1-z^2)(1-2z^2-tz^3)/(1-4z^2-z-tz+2tz^4+4z^4-z^6 +2z^3+tz^3+t^2*z^3). EXAMPLE T(4,2)=2 because we have UDUU|DU|DD and UU|DDUU|DD, where U=(1,1) and D=(1,-1) (the peaks at even level are shown by a |). Triangle starts: 1; 1,1; 2,2,1; 4,6,2,1; 8,13,10,2,1; 16,34,23,13,2,1; MAPLE G:=z*(1-z^2)*(1-2*z^2-t*z^3)/(1-4*z^2-z-t*z+2*t*z^4+4*z^4-z^6+2*z^3+t*z^3+z^3*t^2): Gser:=simplify(series(G, z=0, 15)): P[0]:=1: for n from 1 to 12 do P[n]:=sort(coeff(Gser, z^n)) od: for n from 0 to 12 do seq(coeff(P[n], t, j), j=0..n-1) od; # yields sequence in triangular form CROSSREFS Cf. A001519, A121481, A121485, A121486. Sequence in context: A330843 A115313 A048942 * A273903 A346420 A080928 Adjacent sequences: A121481 A121482 A121483 * A121485 A121486 A121487 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Aug 02 2006 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 May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)