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A316427 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 7

%I #4 Jul 02 2018 09:14:24

%S 1,2,2,3,5,3,5,9,9,5,8,21,14,21,8,13,53,32,32,53,13,21,105,75,97,75,

%T 105,21,34,237,148,279,279,148,237,34,55,577,311,640,1097,640,311,577,

%U 55,89,1205,687,1660,2861,2861,1660,687,1205,89,144,2681,1443,4353,8761,8916

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

%C Table starts

%C ..1....2....3.....5.....8.....13......21.......34.......55........89........144

%C ..2....5....9....21....53....105.....237......577.....1205......2681.......6349

%C ..3....9...14....32....75....148.....311......687.....1443......3042.......6534

%C ..5...21...32....97...279....640....1660.....4353....10975.....28038......72143

%C ..8...53...75...279..1097...2861....8761....29548....87743....267014.....852011

%C .13..105..148...640..2861...8916...31433...121028...417457...1475614....5432803

%C .21..237..311..1660..8761..31433..130402...585212..2366785...9815061...42205654

%C .34..577..687..4353.29548.121028..585212..3242010.15459503..75494391..392102065

%C .55.1205.1443.10975.87743.417457.2366785.15459503.86620644.498441146.3054494072

%H R. H. Hardin, <a href="/A316427/b316427.txt">Table of n, a(n) for n = 1..263</a>

%F Empirical for column k:

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

%F k=2: a(n) = a(n-1) +8*a(n-3) -4*a(n-4)

%F k=3: [order 12]

%F k=4: [order 42] for n>43

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A303963.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 02 2018

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Last modified April 14 10:04 EDT 2024. Contains 371657 sequences. (Running on oeis4.)