The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A222444 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A222444

T(n,k) = number of n X k 0..3 arrays with entries increasing mod 4 by 0, 1 or 2 rightwards and downwards, starting with upper left zero.
(history; published version)

#18 by Charles R Greathouse IV at Sun Feb 16 08:33:19 EST 2025

LINKS

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/VertexColoring.html">Vertex Coloring</a>

Discussion

Sun Feb 16

08:33

OEIS Server: https://oeis.org/edit/global/3014

#17 by OEIS Server at Wed Jun 28 02:35:12 EDT 2017

LINKS

Andrew Howroyd, <a href="/A222444/b222444_1.txt">Table of n, a(n) for n = 1..496</a> (terms 1..180 from R. H. Hardin)

#16 by Michel Marcus at Wed Jun 28 02:35:12 EDT 2017

STATUS

reviewed

approved

Discussion

Wed Jun 28

02:35

OEIS Server: Installed new b-file as b222444.txt.  Old b-file is now b222444_1.txt.

#15 by Joerg Arndt at Wed Jun 28 02:14:26 EDT 2017

STATUS

proposed

reviewed

#14 by Jon E. Schoenfield at Wed Jun 28 00:16:24 EDT 2017

STATUS

editing

proposed

#13 by Jon E. Schoenfield at Wed Jun 28 00:16:20 EDT 2017

NAME

T(n,k) =Number number of nXk n X k 0..3 arrays with entries increasing mod 4 by 0, 1 or 2 rightwards and downwards, starting with upper left zero.

FORMULA

k=3: a(n) = 18*a(n-1) - 27*a(n-2).

k=4: a(n) = 45*a(n-1) - 267*a(n-2) + 263*a(n-3).

k=5: a(n) = 118*a(n-1) - 2811*a(n-2) + 22255*a(n-3) - 53860*a(n-4) - 54747*a(n-5) + 269406*a(n-6) - 175392*a(n-7).

EXAMPLE

Some solutions for n=3 , k=4:

STATUS

proposed

editing

#12 by Andrew Howroyd at Tue Jun 27 12:37:09 EDT 2017

STATUS

editing

proposed

#11 by Andrew Howroyd at Tue Jun 27 12:35:05 EDT 2017

FORMULA

T(n,k) = 6*A198715(n,k) - 3 for n*k>1. - Andrew Howroyd, Jun 27 2017

CROSSREFS

Columns 1-7 are A000244(n-1), A169634(n-1), A222439, A222440, A222441-, A222442, A222443.

STATUS

proposed

editing

#10 by Andrew Howroyd at Tue Jun 27 11:07:36 EDT 2017

STATUS

editing

proposed

#9 by Andrew Howroyd at Tue Jun 27 11:06:13 EDT 2017

CROSSREFS

Columns 1-7 are A000244(n-1), A169634(n-1), A222439, A222440, A222441-A222442A222443.