The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A348595 Triangle read by rows: Number of walks from (0,0) to (3n,3k) on the square lattice with up and right steps where squares (x,y)=(1,1) mod 3 or (x,y)=(2,2) mod 3 are not entered. 3
 1, 1, 4, 1, 8, 28, 1, 12, 64, 212, 1, 16, 116, 520, 1676, 1, 20, 184, 1052, 4288, 13604, 1, 24, 268, 1872, 9316, 35784, 112380, 1, 28, 368, 3044, 17976, 81708, 301440, 940020, 1, 32, 484, 4632, 31740, 167376, 713940, 2558280, 7936620, 1, 36, 616, 6700, 52336, 314932, 1531000, 6231100, 21842560, 67494980 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..54. R. J. Mathar, Walks of up and right steps in the square lattice with blocked squares FORMULA G.f.: (1-u*v)/(1-u-v-3*u*v) . EXAMPLE The array is symmetric; the non-redundant triangular part starts 1 1 4 1 8 28 1 12 64 212 1 16 116 520 1676 1 20 184 1052 4288 13604 1 24 268 1872 9316 35784 112380 1 28 368 3044 17976 81708 301440 940020 1 32 484 4632 31740 167376 713940 2558280 7936620 MAPLE A348595 := proc(n, k) g := (1-u*v)/(1-u-v-3*u*v) ; coeftayl(%, u=0, n) ; coeftayl(%, v=0, k) ; end proc: seq(seq( A348595(n, k), k=0..n), n=0..10) ; MATHEMATICA T[n_, k_] := Module[{u, v}, SeriesCoefficient[(1 - u v)/(1 - u - v - 3 u v), {u, 0, n}] // SeriesCoefficient[#, {v, 0, k}]&]; Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Aug 16 2023 *) CROSSREFS Cf. A085363 (diagonal), A307584 (walks to (3n+1,3k)) Sequence in context: A366399 A100235 A089072 * A036177 A360131 A177841 Adjacent sequences: A348592 A348593 A348594 * A348596 A348597 A348598 KEYWORD nonn,tabl,easy AUTHOR R. J. Mathar, Jan 26 2022 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 November 28 22:38 EST 2023. Contains 367422 sequences. (Running on oeis4.)