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A316925 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 7

%I #4 Jul 16 2018 12:53:54

%S 1,2,2,3,5,3,5,9,9,5,8,21,13,21,8,13,57,31,31,57,13,21,125,81,137,81,

%T 125,21,34,289,184,594,594,184,289,34,55,741,492,2574,6339,2574,492,

%U 741,55,89,1737,1457,15118,40938,40938,15118,1457,1737,89,144,4045,4371,95244

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

%C Table starts

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

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

%C ..3....9...13.....31.......81........184..........492............1457

%C ..5...21...31....137......594.......2574........15118...........95244

%C ..8...57...81....594.....6339......40938.......428394.........5627600

%C .13..125..184...2574....40938.....533726.....11571636.......256609365

%C .21..289..492..15118...428394...11571636....493774680.....20147703090

%C .34..741.1457..95244..5627600..256609365..20147703090...1580858618327

%C .55.1737.4371.569635.59111561.5035506864.740128547549.105913781465166

%H R. H. Hardin, <a href="/A316925/b316925.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 17] for n>19

%F k=4: [order 51] for n>55

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A304349.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 16 2018

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Last modified May 25 03:08 EDT 2024. Contains 372782 sequences. (Running on oeis4.)