A301361 - OEIS

%I #4 Mar 19 2018 09:57:35

%S 0,1,1,1,2,1,2,6,6,2,3,15,13,15,3,5,37,34,34,37,5,8,90,92,101,92,90,8,

%T 13,223,256,320,320,256,223,13,21,550,721,1167,1356,1167,721,550,21,

%U 34,1355,2036,3961,6279,6279,3961,2036,1355,34,55,3341,5701,13974,30236,44148

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

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

%C ..1....2....6....15.....37.......90.......223........550.........1355

%C ..1....6...13....34.....92......256.......721.......2036.........5701

%C ..2...15...34...101....320.....1167......3961......13974........49388

%C ..3...37...92...320...1356.....6279.....30236.....147448.......713700

%C ..5...90..256..1167...6279....44148....317019....2249565.....15884635

%C ..8..223..721..3961..30236...317019...3241470...32453379....325518524

%C .13..550.2036.13974.147448..2249565..32453379..456790733...6500634810

%C .21.1355.5701.49388.713700.15884635.325518524.6500634810.132506438551

%H R. H. Hardin, <a href="/A301361/b301361.txt">Table of n, a(n) for n = 1..219</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) +2*a(n-2) +3*a(n-3) +2*a(n-4) +a(n-5)

%F k=3: [order 31]

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A300344.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 19 2018