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A231131 T(n,k) = Number of (n+1) X (k+1) white-square subarrays of 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

%I A231131 #6 Jun 19 2025 21:05:06
%S A231131 1,2,2,6,8,6,16,40,40,16,44,176,308,176,44,120,808,2260,2260,808,120,
%T A231131 328,3584,16812,27664,16812,3584,328,896,16368,124644,336004,336004,
%U A231131 124644,16368,896,2448,72640,924900,4150352,6794904,4150352,924900,72640,2448
%N A231131 T(n,k) = Number of (n+1) X (k+1) white-square subarrays of 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
%C A231131 Table starts
%C A231131 ..1...2.....6.....16......44.......120........328.........896..........2448
%C A231131 ..2...8....40....176.....808......3584......16368.......72640........331648
%C A231131 ..6..40...308...2260...16812....124644.....924900.....6862052......50913012
%C A231131 .16.176..2260..27664..336004...4150352...50257244...621150768....7520563372
%C A231131 .44.808.16812.336004.6794904.137063228.2766762720.55844298404.1127200291672
%H A231131 R. H. Hardin, <a href="/A231131/b231131.txt">Table of n, a(n) for n = 1..312</a>
%F A231131 Empirical for column k:
%F A231131 k=1: a(n) = 2*a(n-1) +2*a(n-2);
%F A231131 k=2: a(n) = 22*a(n-2) -36*a(n-4) +16*a(n-6);
%F A231131 k=3: [order 8];
%F A231131 k=4: [order 18, even terms];
%F A231131 k=5: [order 34];
%F A231131 k=6: [order 90, even terms].
%e A231131 Some solutions for n=2, k=4
%e A231131 ..0..x..1..x..1....0..x..0..x..1....0..x..1..x..0....0..x..0..x..1
%e A231131 ..x..1..x..2..x....x..1..x..0..x....x..1..x..2..x....x..1..x..2..x
%e A231131 ..2..x..2..x..1....2..x..1..x..1....0..x..0..x..0....0..x..2..x..1
%Y A231131 Column 1 is A002605.
%K A231131 nonn,tabl
%O A231131 1,2
%A A231131 _R. H. Hardin_, Nov 04 2013