A234823 - OEIS

A234823

T(n,k) is the number of (n+1) X (k+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 6 (constant-stress 1 X 1 tilings).

%I #6 Jun 20 2022 20:46:04

%S 168,686,686,2380,2220,2380,9716,6282,6282,9716,34092,22098,15224,

%T 22098,34092,139112,68570,47136,47136,68570,139112,493348,252486,

%U 131704,129384,131704,252486,493348,2011808,828354,443220,325424,325424,443220,828354

%N T(n,k) is the number of (n+1) X (k+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 6 (constant-stress 1 X 1 tilings).

%C Table starts

%C 168 686 2380 9716 34092 139112 493348 2011808

%C 686 2220 6282 22098 68570 252486 828354 3136350

%C 2380 6282 15224 47136 131704 443220 1352816 4791948

%C 9716 22098 47136 129384 325424 994812 2794776 9151956

%C 34092 68570 131704 325424 747192 2099300 5474032 16726940

%C 139112 252486 443220 994812 2099300 5441232 13185612 37597992

%C 493348 828354 1352816 2794776 5474032 13185612 29871848 79958916

%C 2011808 3136350 4791948 9151956 16726940 37597992 79958916 201644928

%C 7205628 10660586 15484360 27722816 47728392 100759412 202105408 481962668

%C 29360336 41107950 56779452 95289828 154893260 307659576 583797684 1320262800

%H R. H. Hardin, <a href="/A234823/b234823.txt">Table of n, a(n) for n = 1..197</a>

%F Empirical for column k (the k=2..6 recurrence also works for column 1; apparently all rows and columns satisfy the same order 23 recurrence):

%F k=1: [linear recurrence of order 7].

%F k=2..6: [same recurrence of order 23].

%e Some solutions for n=4, k=4:

%e 5 0 3 2 4 4 3 6 2 4 3 6 4 5 4 6 0 3 0 4

%e 2 3 0 5 1 1 6 3 5 1 5 2 6 1 6 3 3 0 3 1

%e 6 1 4 3 5 3 2 5 1 3 0 3 1 2 1 6 0 3 0 4

%e 2 3 0 5 1 1 6 3 5 1 4 1 5 0 5 3 3 0 3 1

%e 6 1 4 3 5 3 2 5 1 3 1 4 2 3 2 6 0 3 0 4

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 31 2013