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A235017 T(n,k) is the number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings). 8

%I

%S 40,104,104,264,224,264,680,488,488,680,1736,1112,936,1112,1736,4456,

%T 2568,1912,1912,2568,4456,11400,6088,4008,3560,4008,6088,11400,29224,

%U 14600,8760,6856,6856,8760,14600,29224,74824,35560,19560,13912,12168

%N T(n,k) is the number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%C Table starts

%C 40 104 264 680 1736 4456 11400 29224 74824 191720

%C 104 224 488 1112 2568 6088 14600 35560 87368 216680

%C 264 488 936 1912 4008 8760 19560 44952 105128 250744

%C 680 1112 1912 3560 6856 13912 28968 62600 138360 314376

%C 1736 2568 4008 6856 12168 23016 44680 90824 189032 407880

%C 4456 6088 8760 13912 23016 40968 74888 144184 283832 581720

%C 11400 14600 19560 28968 44680 74888 128776 235240 437928 853928

%C 29224 35560 44952 62600 90824 144184 235240 410760 729688 1363336

%C 74824 87368 105128 138360 189032 283832 437928 729688 1234216 2211128

%C 191720 216680 250744 314376 407880 581720 853928 1363336 2211128 3822728

%H R. H. Hardin, <a href="/A235017/b235017.txt">Table of n, a(n) for n = 1..480</a>

%F Empirical for column k (the k=4..7 recurrence also works for k=1..3; apparently every row and column satisfies the same order 10 recurrence):

%F k=1: a(n) = a(n-1) +4*a(n-2).

%F k=2: a(n) = 3*a(n-1) +4*a(n-2) -14*a(n-3) -4*a(n-4) +16*a(n-5).

%F k=3: [order 8].

%F k=4..7: [same order 10 recurrence].

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

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

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

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

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

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

%Y Column 1 is A185761(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 02 2014

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Last modified October 4 06:54 EDT 2022. Contains 357237 sequences. (Running on oeis4.)