A235198 - OEIS

A235198

T(n,k) is the number of (n+1) X (k+1) 0..6 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 #8 Jun 19 2022 02:21:21

%S 136,512,512,1880,1544,1880,7072,4724,4724,7072,26040,15604,12176,

%T 15604,26040,98080,51144,35868,35868,51144,98080,361688,176104,105208,

%U 96848,105208,176104,361688,1364512,597712,333340,261760,261760,333340,597712

%N T(n,k) is the number of (n+1) X (k+1) 0..6 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 136 512 1880 7072 26040 98080 361688 1364512

%C 512 1544 4724 15604 51144 176104 597712 2109748

%C 1880 4724 12176 35868 105208 333340 1043256 3446068

%C 7072 15604 35868 96848 261760 774140 2263256 7020392

%C 26040 51144 105208 261760 652872 1816160 4984584 14642048

%C 98080 176104 333340 774140 1816160 4812096 12604104 35505020

%C 361688 597712 1043256 2263256 4984584 12604104 31498952 85424552

%C 1364512 2109748 3446068 7020392 14642048 35505020 85424552 224694240

%C 5038200 7324940 11230320 21497244 42396520 98577596 227963432 582078148

%C 19038496 26321996 38241780 68985912 129109408 287939516 642257224 1596252448

%H R. H. Hardin, <a href="/A235198/b235198.txt">Table of n, a(n) for n = 1..197</a>

%F Empirical for column k (the k=3..6 recurrence works also for k=1..2; apparently all rows and columns satisfy the same order 39 recurrence):

%F k=1: a(n) = 30*a(n-2) -257*a(n-4) +468*a(n-6).

%F k=2: [order 23].

%F k=3..6: [same order 39 recurrence].

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 04 2014