A305489 - OEIS

%I #4 Jun 02 2018 09:02:53

%S 0,1,1,1,7,1,2,14,14,2,3,33,19,33,3,5,70,27,27,70,5,8,157,137,65,137,

%T 157,8,13,346,295,195,195,295,346,13,21,769,570,125,2094,125,570,769,

%U 21,34,1710,2026,268,7007,7007,268,2026,1710,34,55,3813,4727,1176,16464,23229

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 6 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0....1....1....2......3.......5.......8........13.........21..........34

%C ..1....7...14...33.....70.....157.....346.......769.......1710........3813

%C ..1...14...19...27....137.....295.....570......2026.......4727.......10623

%C ..2...33...27...65....195.....125.....268......1176........805........1681

%C ..3...70..137..195...2094....7007...16464.....91350.....348956.....1047508

%C ..5..157..295..125...7007...23229...52124....581383....2463954.....8570618

%C ..8..346..570..268..16464...52124...65452...2034173....7974852....20131094

%C .13..769.2026.1176..91350..581383.2034173..35294211..261130745..1568168588

%C .21.1710.4727..805.348956.2463954.7974852.261130745.2468446765.16736271764

%H R. H. Hardin, <a href="/A305489/b305489.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

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

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

%F k=3: [order 14] for n>16

%F k=4: [order 17] for n>22

%F k=5: [order 97] for n>100

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A304143.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jun 02 2018