cp's OEIS Frontend

A231764 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

%I A231764 #6 Jul 23 2025 06:41:16
%S A231764 9,33,16,100,136,36,315,625,660,81,961,2976,5041,3213,169,3024,15625,
%T A231764 38160,40000,14989,361,9409,84817,356409,493695,303601,70927,784,
%U A231764 29319,440896,3453471,8231161,5879679,2353156,338352,1681,91204,2280000
%N A231764 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.
%C A231764 Table starts
%C A231764 ....9.......33........100...........315.............961...............3024
%C A231764 ...16......136........625..........2976...........15625..............84817
%C A231764 ...36......660.......5041.........38160..........356409............3453471
%C A231764 ...81.....3213......40000........493695.........8231161..........143424652
%C A231764 ..169....14989.....303601.......5879679.......175642009.........5493044921
%C A231764 ..361....70927....2353156......71884125......3855664836.......216545491864
%C A231764 ..784...338352...18318400.....893571840.....85629975876......8624298007460
%C A231764 .1681..1603633..141681409...10965349591...1881009507001....340129511751843
%C A231764 .3600..7596720.1096603225..134407778400..41320353904281..13416072442152345
%C A231764 .7744.36066272.8501393209.1654812479232.910635938795025.530629269304561623
%H A231764 R. H. Hardin, <a href="/A231764/b231764.txt">Table of n, a(n) for n = 1..219</a>
%F A231764 Empirical for column k:
%F A231764 k=1: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6)
%F A231764 k=2: [order 21]
%F A231764 k=3: [order 45]
%F A231764 Empirical for row n:
%F A231764 n=1: a(n) = 3*a(n-1) +a(n-3) +7*a(n-4) -20*a(n-5) -2*a(n-6) -4*a(n-8) +8*a(n-9)
%F A231764 n=2: [order 36]
%e A231764 Some solutions for n=3 k=4
%e A231764 ..0..1..0..1..1....1..1..1..0..1....0..0..0..0..1....0..1..1..1..0
%e A231764 ..1..0..0..0..0....0..0..0..1..0....0..0..1..0..0....0..0..1..0..0
%e A231764 ..1..0..0..0..1....0..0..0..0..0....0..0..0..1..1....1..0..0..0..0
%e A231764 ..1..0..0..0..0....0..0..0..0..0....1..1..0..0..1....1..0..0..1..1
%Y A231764 Column 1 is A207170 for n>1
%K A231764 nonn,tabl
%O A231764 1,1
%A A231764 _R. H. Hardin_, Nov 13 2013