A235212 - OEIS

A235212

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 5, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%I #7 Jun 19 2022 00:09:30

%S 240,1172,1172,5696,4616,5696,27812,18444,18444,27812,135520,76112,

%T 61160,76112,135520,662892,319156,215996,215996,319156,662892,3236288,

%U 1374400,781040,672256,781040,1374400,3236288,15860868,5998924,2971196,2154516

%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 5, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%C Table starts

%C 240 1172 5696 27812 135520 662892 3236288

%C 1172 4616 18444 76112 319156 1374400 5998924

%C 5696 18444 61160 215996 781040 2971196 11553392

%C 27812 76112 215996 672256 2154516 7402144 26061700

%C 135520 319156 781040 2154516 6122960 19043548 60655008

%C 662892 1374400 2971196 7402144 19043548 54586424 160144012

%C 3236288 5998924 11553392 26061700 60655008 160144012 432038320

%C 15860868 26765648 46833260 96901472 207093844 509661968 1282142052

%C 77573344 120643572 193465560 368028508 721977376 1652364332 3864421920

%C 380902284 553515168 826218532 1459917480 2659371660 5703493096 12517909388

%H R. H. Hardin, <a href="/A235212/b235212.txt">Table of n, a(n) for n = 1..142</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) +35*a(n-2) -81*a(n-3) -264*a(n-4) +144*a(n-5) +384*a(n-6).

%F k=2: [order 29].

%F k=3: [order 62].

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 04 2014