A301354 - OEIS

%I #4 Mar 19 2018 09:46:12

%S 0,1,1,1,3,1,2,10,10,2,3,30,53,30,3,5,96,277,277,96,5,8,307,1433,2349,

%T 1433,307,8,13,981,7522,19561,19561,7522,981,13,21,3137,39390,165010,

%U 264054,165010,39390,3137,21,34,10034,206370,1392131,3579171,3579171

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ..0.....1.......1........2..........3............5..............8

%C ..1.....3......10.......30.........96..........307............981

%C ..1....10......53......277.......1433.........7522..........39390

%C ..2....30.....277.....2349......19561.......165010........1392131

%C ..3....96....1433....19561.....264054......3579171.......48476633

%C ..5...307....7522...165010....3579171.....78012336.....1702789144

%C ..8...981...39390..1392131...48476633...1702789144....59990521481

%C .13..3137..206370.11741731..656551657..37169645074..2112136719464

%C .21.10034.1081141.99032014.8891966361.811102103620.74331048515102

%H R. H. Hardin, <a href="/A301354/b301354.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2)

%F k=2: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6) for n>7

%F k=3: [order 18] for n>20

%F k=4: [order 72] for n>73

%e Some solutions for n=5 k=4

%e ..0..1..1..1. .0..0..1..0. .0..0..1..1. .0..1..1..1. .0..0..0..1

%e ..0..0..0..0. .1..0..1..0. .1..1..1..1. .0..0..1..0. .1..1..0..1

%e ..0..1..0..0. .1..0..0..0. .0..0..1..0. .0..1..0..1. .1..1..0..0

%e ..0..1..1..0. .0..1..1..1. .0..1..0..1. .0..0..0..1. .0..1..1..0

%e ..0..1..0..0. .0..1..0..0. .1..1..1..1. .1..1..0..0. .0..1..1..0

%Y Column 1 is A000045(n-1).

%Y Column 2 is A300421.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 19 2018