A305340 - OEIS

%I #4 May 30 2018 16:59:04

%S 1,2,2,4,4,4,8,5,5,8,16,9,12,9,16,32,22,26,26,22,32,64,45,62,81,62,45,

%T 64,128,101,166,267,267,166,101,128,256,218,431,938,1185,938,431,218,

%U 256,512,477,1091,3186,5296,5296,3186,1091,477,512,1024,1041,2812,10840

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1...2....4.....8.....16......32.......64.......128.........256..........512

%C ...2...4....5.....9.....22......45......101.......218.........477.........1041

%C ...4...5...12....26.....62.....166......431......1091........2812.........7268

%C ...8...9...26....81....267.....938.....3186.....10840.......37115.......127093

%C ..16..22...62...267...1185....5296....23348....103641......460756......2046399

%C ..32..45..166...938...5296...30826...176673...1020555.....5903993.....34127533

%C ..64.101..431..3186..23348..176673..1321695...9959836....75112075....566241938

%C .128.218.1091.10840.103641.1020555..9959836..98008416...964336401...9486731570

%C .256.477.2812.37115.460756.5903993.75112075.964336401.12373093291.158745150050

%H R. H. Hardin, <a href="/A305340/b305340.txt">Table of n, a(n) for n = 1..391</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = a(n-1) +3*a(n-2) +3*a(n-3) +2*a(n-4) -3*a(n-5) -8*a(n-6) -4*a(n-7) for n>8

%F k=4: [order 15] for n>19

%F k=5: [order 32] for n>34

%F k=6: [order 62] for n>66

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A052962 for n>2.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, May 30 2018