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 A297823 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 king-move adjacent elements, with upper left element zero. 8

%I #4 Jan 06 2018 10:59:10

%S 0,1,1,1,4,1,2,17,17,2,3,49,48,49,3,5,166,146,146,166,5,8,573,399,466,

%T 399,573,8,13,1933,1114,1395,1395,1114,1933,13,21,6538,3124,4306,4444,

%U 4306,3124,6538,21,34,22165,8861,13417,14237,14237,13417,8861,22165,34

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

%C Table starts

%C ..0.....1.....1......2......3.......5.......8.......13.......21........34

%C ..1.....4....17.....49....166.....573....1933.....6538....22165.....75089

%C ..1....17....48....146....399....1114....3124.....8861....25130.....71196

%C ..2....49...146....466...1395....4306...13417....41512...128084....395130

%C ..3...166...399...1395...4444...14237...43931...134395...412427...1268252

%C ..5...573..1114...4306..14237...46701..146530...456814..1433279...4501076

%C ..8..1933..3124..13417..43931..146530..467104..1485611..4742326..15121792

%C .13..6538..8861..41512.134395..456814.1485611..4833331.15742632..51146914

%C .21.22165.25130.128084.412427.1433279.4742326.15742632.52153064.172452330

%H R. H. Hardin, <a href="/A297823/b297823.txt">Table of n, a(n) for n = 1..449</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6

%F k=3: [order 9] for n>11

%F k=4: [order 18] for n>21

%F k=5: [order 49] for n>55

%F k=6: [order 98] for n>107

%e Some solutions for n=6 k=4

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

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

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 06 2018

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Last modified September 27 19:23 EDT 2023. Contains 365714 sequences. (Running on oeis4.)