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A235310 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 6 (constant-stress 1 X 1 tilings). 9

%I

%S 70,210,210,518,518,518,1554,1106,1106,1554,4006,2918,2118,2918,4006,

%T 12018,6786,5042,5042,6786,12018,32006,18662,10790,10790,10790,18662,

%U 32006,96018,46226,27602,21090,21090,27602,46226,96018,261670,130598

%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 6 (constant-stress 1 X 1 tilings).

%C Table starts

%C 70 210 518 1554 4006 12018 32006 96018 261670

%C 210 518 1106 2918 6786 18662 46226 130598 338370

%C 518 1106 2118 5042 10790 27602 64326 172658 428198

%C 1554 2918 5042 10790 21090 49574 107186 269222 629154

%C 4006 6786 10790 21090 38182 83394 168998 400674 889126

%C 12018 18662 27602 49574 83394 168998 319826 711206 1486338

%C 32006 46226 64326 107186 168998 319826 568902 1192946 2360486

%C 96018 130598 172658 269222 400674 711206 1192946 2360486 4418658

%C 261670 338370 428198 629154 889126 1486338 2360486 4418658 7845670

%C 785010 973478 1187666 1656998 2238786 3544742 5359826 9528998 16106370

%C Empirical: T(n,k) is the number of (n+1) X (k+1) 0..4+i arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4+2*i (constant-stress 1 X 1 tilings), for i=1..3(..?).

%H R. H. Hardin, <a href="/A235310/b235310.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k (the k=2..7 recurrence also works for k=1; apparently all rows and columns satisfy the same order 14 recurrence):

%F k=1: a(n) = 3*a(n-1) +13*a(n-2) -39*a(n-3) -40*a(n-4) +120*a(n-5)

%F k=2..7: [same order 14 recurrence]

%e Some solutions for n=5, k=4:

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 05 2014

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Last modified October 7 05:49 EDT 2022. Contains 357270 sequences. (Running on oeis4.)