A304931 - OEIS

%I #4 May 21 2018 09:24:16

%S 1,2,2,3,5,3,5,9,9,5,8,21,13,21,8,13,53,26,26,53,13,21,105,54,73,54,

%T 105,21,34,237,101,173,173,101,237,34,55,577,186,374,452,374,186,577,

%U 55,89,1205,361,842,1034,1034,842,361,1205,89,144,2681,700,1923,2265,2653,2265

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 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......89.....144......233

%C ..2....5...9...21....53...105....237....577...1205....2681....6349....13681

%C ..3....9..13...26....54...101....186....361....700....1340....2562.....4913

%C ..5...21..26...73...173...374....842...1923...4326....9786...22216....50282

%C ..8...53..54..173...452..1034...2265...5306..12135...28127...66067...153211

%C .13..105.101..374..1034..2653...6426..16855..42256..110818..293243...759597

%C .21..237.186..842..2265..6426..15993..42032.107527..294610..802939..2150494

%C .34..577.361.1923..5306.16855..42032.118024.317161..963090.2839363..8199638

%C .55.1205.700.4326.12135.42256.107527.317161.920997.3074573.9708161.30250926

%H R. H. Hardin, <a href="/A304931/b304931.txt">Table of n, a(n) for n = 1..391</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: a(n) = a(n-1) +2*a(n-3) +2*a(n-4) +a(n-5) +a(n-6) -a(n-7) -a(n-11) -a(n-12)

%F k=4: [order 36] for n>37

%F k=5: [order 34] for n>45

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A303963.

%Y Column 3 is A303964.

%Y Column 4 is A303965.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, May 21 2018