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 A300175 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 7

%I #4 Feb 27 2018 12:20:06

%S 0,0,0,0,1,0,0,3,3,0,0,6,9,6,0,0,17,37,37,17,0,0,41,192,268,192,41,0,

%T 0,104,932,2620,2620,932,104,0,0,261,4712,23522,50419,23522,4712,261,

%U 0,0,655,23795,223445,886940,886940,223445,23795,655,0,0,1646,120610,2117743

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .0...0......0........0..........0.............0...............0

%C .0...1......3........6.........17............41.............104

%C .0...3......9.......37........192...........932............4712

%C .0...6.....37......268.......2620.........23522..........223445

%C .0..17....192.....2620......50419........886940........16262433

%C .0..41....932....23522.....886940......30129628......1068913988

%C .0.104...4712...223445...16262433....1068913988.....73267622156

%C .0.261..23795..2117743..297460457...37795185266...5003777484149

%C .0.655.120610.20154626.5454615441.1339340557254.342457741960757

%H R. H. Hardin, <a href="/A300175/b300175.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

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

%F k=3: [order 11] for n>13

%F k=4: [order 25] for n>26

%F k=5: [order 66] for n>69

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A297972.

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Feb 27 2018

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Last modified September 8 20:40 EDT 2024. Contains 375759 sequences. (Running on oeis4.)