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A298230 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero. 7

%I #4 Jan 15 2018 08:53:31

%S 1,2,2,3,4,3,5,4,4,5,8,16,5,16,8,13,50,17,17,50,13,21,112,12,195,12,

%T 112,21,34,348,100,490,490,100,348,34,55,1028,219,2606,1749,2606,219,

%U 1028,55,89,2796,498,15646,7038,7038,15646,498,2796,89,144,8216,1999,74688,71212

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

%C Table starts

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

%C ..2....4....4.....16......50.......112........348.........1028...........2796

%C ..3....4....5.....17......12.......100........219..........498...........1999

%C ..5...16...17....195.....490......2606......15646........74688.........397909

%C ..8...50...12....490....1749......7038......71212.......440402........2785299

%C .13..112..100...2606....7038....110320....1166270.....10448313......136604409

%C .21..348..219..15646...71212...1166270...25406586....353699661.....6688607300

%C .34.1028..498..74688..440402..10448313..353699661...7311722995...215277571718

%C .55.2796.1999.397909.2785299.136604409.6688607300.215277571718.11308912804354

%H R. H. Hardin, <a href="/A298230/b298230.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) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

%F k=3: [order 18] for n>19

%F k=4: [order 66] for n>68

%e Some solutions for n=6 k=4

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

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

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

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

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

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

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

%Y Column 2 is A298148.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jan 15 2018

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Last modified February 26 17:57 EST 2024. Contains 370352 sequences. (Running on oeis4.)