cp's OEIS Frontend

A268750 T(n,k)=Number of nXk binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

%I A268750 #4 Feb 12 2016 12:34:24
%S A268750 2,4,4,7,11,7,13,32,32,13,23,89,143,89,23,41,244,623,623,244,41,72,
%T A268750 659,2615,4110,2615,659,72,126,1760,10830,26334,26334,10830,1760,126,
%U A268750 219,4657,44067,165019,255651,165019,44067,4657,219,379,12228,177429,1016807
%N A268750 T(n,k)=Number of nXk binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.
%C A268750 Table starts
%C A268750 ...2.....4.......7........13..........23............41.............72
%C A268750 ...4....11......32........89.........244...........659...........1760
%C A268750 ...7....32.....143.......623........2615.........10830..........44067
%C A268750 ..13....89.....623......4110.......26334........165019........1016807
%C A268750 ..23...244....2615.....26334......255651.......2425799.......22577073
%C A268750 ..41...659...10830....165019.....2425799......34732937......487682438
%C A268750 ..72..1760...44067...1016807....22577073.....487682438....10319681062
%C A268750 .126..4657..177429...6183665...207252725....6746117783...215027310572
%C A268750 .219.12228..707163..37209717..1880654551...92215499119..4425392044505
%C A268750 .379.31899.2796840.221970102.16909709308.1248437108837.90177748184504
%H A268750 R. H. Hardin, <a href="/A268750/b268750.txt">Table of n, a(n) for n = 1..1404</a>
%F A268750 Empirical for column k:
%F A268750 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F A268750 k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) -a(n-4)
%F A268750 k=3: a(n) = 4*a(n-1) +8*a(n-2) -24*a(n-3) -38*a(n-4) +4*a(n-5) +12*a(n-6) -a(n-8)
%F A268750 k=4: [order 10]
%F A268750 k=5: [order 18]
%F A268750 k=6: [order 22]
%F A268750 k=7: [order 42]
%e A268750 Some solutions for n=4 k=4
%e A268750 ..1..0..0..0. .0..0..0..0. .1..0..1..0. .0..1..0..0. .0..1..0..0
%e A268750 ..0..1..0..1. .0..0..0..0. .0..1..0..0. .0..0..1..0. .1..0..1..0
%e A268750 ..1..0..0..0. .1..0..0..0. .0..0..0..0. .0..1..0..0. .0..1..0..0
%e A268750 ..0..0..0..1. .0..1..1..0. .0..1..0..1. .1..0..0..0. .1..0..0..0
%Y A268750 Column 1 is A208354(n+1).
%K A268750 nonn,tabl
%O A268750 1,1
%A A268750 _R. H. Hardin_, Feb 12 2016