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A234991 T(n,k) is the number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings). 9

%I #6 Jun 20 2022 20:39:36

%S 90,370,370,1640,1490,1640,7554,6908,6908,7554,35072,35598,34608,

%T 35598,35072,163416,189200,206556,206556,189200,163416,762002,1026784,

%U 1303920,1525462,1303920,1026784,762002,3554334,5628414,8616068,12242044

%N T(n,k) is the number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%C Table starts

%C 90 370 1640 7554 35072 163416

%C 370 1490 6908 35598 189200 1026784

%C 1640 6908 34608 206556 1303920 8616068

%C 7554 35598 206556 1525462 12242044 105948984

%C 35072 189200 1303920 12242044 128653892 1507413164

%C 163416 1026784 8616068 105948984 1507413164 24740904388

%C 762002 5628414 58209538 951853990 18608169852 433293595046

%C 3554334 31099742 400984904 8853338774 241470307440 8076317372004

%C 16580250 172847074 2799816642 84210673350 3223991647750 155302530533130

%C 77345792 965377320 19780619488 816873730308 44160189525640 3074015131838128

%H R. H. Hardin, <a href="/A234991/b234991.txt">Table of n, a(n) for n = 1..127</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 8].

%F k=2: [order 28].

%F k=3: [order 91].

%e Some solutions for n=3, k=4:

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 02 2014

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Last modified June 7 04:05 EDT 2024. Contains 373140 sequences. (Running on oeis4.)