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 A235258 T(n,k) is the number of (n+1) X (k+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 7, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings). 9

%I #7 Jun 18 2022 23:45:43

%S 184,744,744,2672,2592,2672,10820,8328,8328,10820,39680,30300,24232,

%T 30300,39680,161060,102000,80812,80812,102000,161060,600928,382036,

%U 251656,247368,251656,382036,600928,2443916,1330480,878988,717452,717452

%N T(n,k) is the number of (n+1) X (k+1) 0..7 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 7, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%C Table starts

%C 184 744 2672 10820 39680 161060 600928

%C 744 2592 8328 30300 102000 382036 1330480

%C 2672 8328 24232 80812 251656 878988 2873128

%C 10820 30300 80812 247368 717452 2337832 7200188

%C 39680 102000 251656 717452 1951752 5990204 17480904

%C 161060 382036 878988 2337832 5990204 17318888 47995084

%C 600928 1330480 2873128 7200188 17480904 47995084 126993640

%C 2443916 5080484 10362212 24526880 56590772 147612912 373324260

%C 9247456 18163048 35132248 79038828 174061880 434010540 1053946488

%C 37667316 70306060 129681452 278130808 586251132 1398866408 3264942732

%H R. H. Hardin, <a href="/A235258/b235258.txt">Table of n, a(n) for n = 1..160</a>

%F Empirical for column k (the k=4..5 recurrence also works for k=1..3; apparently all rows and columns satisfy the same order 58 recurrence):

%F k=1: a(n) = 43*a(n-2) -617*a(n-4) +3073*a(n-6) -1762*a(n-8) +264*a(n-10).

%F k=2: [order 40].

%F k=3: [order 57].

%F k=4..5: [same order 58 recurrence].

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

%e 3 0 5 1 5 6 3 7 2 6 5 1 7 1 7 1 4 0 5 2

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

%e 4 1 6 2 6 5 2 6 1 5 4 0 6 0 6 3 6 2 7 4

%e 2 6 4 7 4 3 7 4 6 3 3 6 5 6 5 5 1 4 2 6

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 05 2014

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Last modified December 7 18:28 EST 2023. Contains 367660 sequences. (Running on oeis4.)