The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A348595

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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.
(history; published version)

#15 by Michael De Vlieger at Wed Aug 16 08:22:03 EDT 2023

STATUS

reviewed

approved

#14 by Michel Marcus at Wed Aug 16 03:25:05 EDT 2023

STATUS

proposed

reviewed

#13 by Jean-François Alcover at Wed Aug 16 03:23:47 EDT 2023

STATUS

editing

proposed

#12 by Jean-François Alcover at Wed Aug 16 03:23:23 EDT 2023

DATA

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

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 *)

STATUS

approved

editing

Discussion

Wed Aug 16

03:23

Jean-François Alcover: Completed last row of data

#11 by Michael De Vlieger at Wed Jan 26 17:57:57 EST 2022

STATUS

proposed

approved

#10 by Michel Marcus at Wed Jan 26 17:23:01 EST 2022

STATUS

editing

proposed

#9 by Michel Marcus at Wed Jan 26 17:22:58 EST 2022

EXAMPLE

The array is symmetric; the non-redudant redundant triangular part starts

1

STATUS

approved

editing

#8 by R. J. Mathar at Wed Jan 26 09:33:26 EST 2022

STATUS

editing

approved

#7 by R. J. Mathar at Wed Jan 26 09:32:29 EST 2022

EXAMPLE

The array is symmetric; the non-redudant 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

#6 by R. J. Mathar at Wed Jan 26 09:31:11 EST 2022

DATA

LINKS

R. J. Mathar, <a href="/A348595/a348595.pdf">Walks of up and right steps in the square lattice with blocked squares</a>