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 A305918 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero. 7

%I #4 Jun 14 2018 07:08:40

%S 1,2,2,3,5,3,5,9,9,5,8,21,13,21,8,13,57,27,27,57,13,21,125,62,101,62,

%T 125,21,34,289,135,347,347,135,289,34,55,741,312,1129,2014,1129,312,

%U 741,55,89,1737,825,4982,8135,8135,4982,825,1737,89,144,4045,2367,23181,57465

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

%C Table starts

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

%C ..2....5....9.....21......57.......125........289..........741...........1737

%C ..3....9...13.....27......62.......135........312..........825...........2367

%C ..5...21...27....101.....347......1129.......4982........23181.........101615

%C ..8...57...62....347....2014......8135......57465.......489154........3344053

%C .13..125..135...1129....8135.....61467.....811996......9980597......112886453

%C .21..289..312...4982...57465....811996...18643274....371733699.....6830409319

%C .34..741..825..23181..489154...9980597..371733699..12581159370...364289254793

%C .55.1737.2367.101615.3344053.112886453.6830409319.364289254793.17019760656259

%H R. H. Hardin, <a href="/A305918/b305918.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) = 2*a(n-1) -a(n-2) +8*a(n-3) -8*a(n-4)

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

%F k=4: [order 66] for n>69

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A304349.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jun 14 2018

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Last modified August 13 11:56 EDT 2024. Contains 375138 sequences. (Running on oeis4.)