cp's OEIS Frontend

A231137 T(n,k)=Number of (n+1)X(k+1) black-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 A231137 #6 Jul 23 2025 06:16:46
%S A231137 1,2,2,6,9,6,16,40,40,16,44,182,308,182,44,120,808,2260,2260,808,120,
%T A231137 328,3688,16812,27171,16812,3688,328,896,16368,124644,336004,336004,
%U A231137 124644,16368,896,2448,74728,924900,4066129,6794904,4066129,924900,74728,2448
%N A231137 T(n,k)=Number of (n+1)X(k+1) black-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 A231137 Table starts
%C A231137 ..1...2.....6.....16......44.......120........328.........896..........2448
%C A231137 ..2...9....40....182.....808......3688......16368.......74728........331648
%C A231137 ..6..40...308...2260...16812....124644.....924900.....6862052......50913012
%C A231137 .16.182..2260..27171..336004...4066129...50257244...608468617....7520563372
%C A231137 .44.808.16812.336004.6794904.137063228.2766762720.55844298404.1127200291672
%H A231137 R. H. Hardin, <a href="/A231137/b231137.txt">Table of n, a(n) for n = 1..312</a>
%F A231137 Empirical for column k:
%F A231137 k=1: a(n) = 2*a(n-1) +2*a(n-2)
%F A231137 k=2: a(n) = 22*a(n-2) -36*a(n-4) +16*a(n-6)
%F A231137 k=3: [order 8]
%F A231137 k=4: [order 18, even terms]
%F A231137 k=5: [order 34]
%F A231137 k=6: [order 90, even terms]
%e A231137 Some solutions for n=2 k=4
%e A231137 ..x..0..x..1..x....x..0..x..1..x....x..0..x..0..x....x..0..x..1..x
%e A231137 ..2..x..0..x..1....1..x..0..x..2....1..x..2..x..0....2..x..0..x..2
%e A231137 ..x..0..x..2..x....x..0..x..1..x....x..1..x..2..x....x..1..x..1..x
%Y A231137 Column 1 is A002605
%Y A231137 Column 3 is A231126
%Y A231137 Column 5 is A231128
%Y A231137 Column 7 is A231130
%K A231137 nonn,tabl
%O A231137 1,2
%A A231137 _R. H. Hardin_, Nov 04 2013