|
%I #4 Apr 23 2018 10:41:44
%S 0,1,0,1,3,0,2,7,10,0,3,10,28,23,0,5,27,42,119,61,0,8,45,100,168,541,
%T 162,0,13,98,290,547,902,2327,421,0,21,193,730,2079,4013,3256,10384,
%U 1103,0,34,379,1700,6322,29411,21361,15852,47491,2890,0,55,778,4246,17903
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C .0....1......1......2.......3.........5..........8..........13............21
%C .0....3......7.....10......27........45.........98.........193...........379
%C .0...10.....28.....42.....100.......290........730........1700..........4246
%C .0...23....119....168.....547......2079.......6322.......17903.........53665
%C .0...61....541....902....4013.....29411.....160247......660748.......3071197
%C .0..162...2327...3256...21361....236326....1716995.....8688851......56229035
%C .0..421..10384..15852..115770...2158662...24386918...158640643....1293822589
%C .0.1103..47491..77904..803911..27002794..497878411..4298730424...50946692110
%C .0.2890.208616.314276.4667376.250400003.6748940959.74532460229.1222253462556
%H R. H. Hardin, <a href="/A303410/b303410.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -a(n-4)
%F k=3: [order 18]
%F k=4: [order 72]
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-2)
%F n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
%F n=3: [order 15] for n>17
%F n=4: [order 71] for n>72
%e Some solutions for n=5 k=4
%e ..0..1..0..0. .0..1..1..0. .0..1..0..1. .0..0..0..0. .0..0..0..0
%e ..1..0..1..1. .1..0..0..1. .1..0..1..0. .1..1..1..1. .1..0..1..0
%e ..0..0..0..0. .1..1..1..1. .0..1..0..1. .1..0..1..0. .0..1..0..1
%e ..0..1..0..0. .0..1..1..0. .0..0..0..0. .1..1..0..1. .1..1..1..1
%e ..1..0..1..1. .1..0..0..1. .1..1..1..1. .1..0..1..0. .0..0..0..1
%Y Column 2 is A185828.
%Y Column 4 is A302524.
%Y Row 1 is A000045(n-1).
%Y Row 2 is A302279.
%Y Row 3 is A302529.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Apr 23 2018
| 