|
%I #4 Feb 10 2018 10:47:17
%S 0,1,1,1,4,1,2,18,18,2,3,52,57,52,3,5,174,226,226,174,5,8,604,861,
%T 1013,861,604,8,13,2048,3432,5294,5294,3432,2048,13,21,6948,13268,
%U 27639,52002,27639,13268,6948,21,34,23652,51790,139226,402789,402789,139226,51790
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0.....1......1.......2.........3..........5............8............13
%C ..1.....4.....18......52.......174........604.........2048..........6948
%C ..1....18.....57.....226.......861.......3432........13268.........51790
%C ..2....52....226....1013......5294......27639.......139226........713421
%C ..3...174....861....5294.....52002.....402789......2991315......25096585
%C ..5...604...3432...27639....402789....4175049.....41279802.....478753977
%C ..8..2048..13268..139226...2991315...41279802....546467591....8711452672
%C .13..6948..51790..713421..25096585..478753977...8711452672..209501211322
%C .21.23652.202533.3674765.203284013.5290010417.130278485534.4519722020986
%H R. H. Hardin, <a href="/A299465/b299465.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
%F k=3: [order 20] for n>21
%F k=4: [order 69] for n>71
%e Some solutions for n=5 k=6
%e ..0..0..1..1..0..1. .0..0..1..1..1..1. .0..0..1..1..1..1. .0..1..1..1..1..0
%e ..0..1..0..1..0..1. .0..0..1..1..1..1. .0..1..0..0..1..0. .0..1..0..0..0..0
%e ..1..0..0..1..0..1. .1..1..1..0..0..0. .1..0..1..1..1..0. .0..1..0..0..0..1
%e ..0..1..0..1..0..1. .1..0..1..1..1..0. .0..1..1..1..0..0. .1..0..0..0..0..1
%e ..1..0..1..1..0..0. .1..0..0..0..0..1. .1..0..1..0..1..1. .0..0..1..1..0..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297945.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Feb 10 2018
| 