|
%I #4 Dec 15 2017 21:17:36
%S 2,4,4,7,11,7,13,31,31,13,24,90,135,90,24,44,254,616,616,254,44,81,
%T 728,2782,4543,2782,728,81,149,2078,12544,32439,32439,12544,2078,149,
%U 274,5931,56646,233636,368720,233636,56646,5931,274,504,16941,255699,1680927
%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 1 or 3 neighboring 1s.
%C Table starts
%C ...2.....4.......7.......13.........24...........44.............81
%C ...4....11......31.......90........254..........728...........2078
%C ...7....31.....135......616.......2782........12544..........56646
%C ..13....90.....616.....4543......32439.......233636........1680927
%C ..24...254....2782....32439.....368720......4215593.......48217515
%C ..44...728...12544...233636....4215593.....76657600.....1394258872
%C ..81..2078...56646..1680927...48217515...1394258872....40337678992
%C .149..5931..255699.12090311..551193737..25339030733..1165868818808
%C .274.16941.1154239.86993766.6302520826.460672241848.33712843195488
%H R. H. Hardin, <a href="/A296578/b296578.txt">Table of n, a(n) for n = 1..311</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2) +a(n-3)
%F k=2: a(n) = a(n-1) +4*a(n-2) +3*a(n-3) +a(n-4) +4*a(n-5) -a(n-6) -6*a(n-7) -a(n-8) +a(n-9)
%F k=3: [order 14]
%F k=4: [order 50]
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..0..0..1. .1..0..0..0. .0..1..0..0. .0..0..1..0
%e ..1..0..0..0. .0..0..1..0. .1..0..0..0. .1..0..0..0. .1..1..0..0
%e ..0..1..0..1. .1..0..0..1. .0..1..0..0. .0..0..0..0. .0..1..0..0
%e ..0..0..0..0. .0..1..0..0. .0..1..0..1. .1..0..0..1. .0..0..1..0
%e ..0..0..1..1. .0..0..1..0. .0..0..0..1. .1..0..0..0. .1..0..1..0
%Y Column 1 is A000073(n+3).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 15 2017
| 