A318037 - OEIS

%I #4 Aug 13 2018 14:25:24

%S 1,2,2,3,3,3,5,6,6,5,8,11,9,11,8,13,22,25,25,22,13,21,46,58,69,58,46,

%T 21,34,91,152,176,176,152,91,34,55,182,368,472,580,472,368,182,55,89,

%U 371,904,1222,1910,1910,1222,904,371,89,144,746,2211,3354,6525,7728,6525

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ..1...2....3....5.....8.....13......21.......34.........55..........89

%C ..2...3....6...11....22.....46......91......182........371.........746

%C ..3...6....9...25....58....152.....368......904.......2211........5420

%C ..5..11...25...69...176....472....1222.....3354.......9209.......25092

%C ..8..22...58..176...580...1910....6525....23463......84609......306640

%C .13..46..152..472..1910...7728...32385...148465.....679005.....3172701

%C .21..91..368.1222..6525..32385..204645..1284756....8133386....51773454

%C .34.182..904.3354.23463.148465.1284756.10928383...94939015...818553114

%C .55.371.2211.9209.84609.679005.8133386.94939015.1157058721.13783060247

%H R. H. Hardin, <a href="/A318037/b318037.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

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

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

%F k=3: [order 30] for n>33

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Aug 13 2018