A299689 - OEIS

%I #4 Feb 16 2018 07:47:19

%S 1,2,2,3,4,3,5,4,4,5,8,16,15,16,8,13,50,54,54,50,13,21,112,156,648,

%T 156,112,21,34,348,854,2850,2850,854,348,34,55,1028,3226,20882,23116,

%U 20882,3226,1028,55,89,2796,13013,159324,251922,251922,159324,13013,2796,89

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C ..2....4.....4......16........50.........112...........348............1028

%C ..3....4....15......54.......156.........854..........3226...........13013

%C ..5...16....54.....648......2850.......20882........159324.........1041908

%C ..8...50...156....2850.....23116......251922.......3247879........36816394

%C .13..112...854...20882....251922.....5740433.....120453362......2322958629

%C .21..348..3226..159324...3247879...120453362....4582634341....154482346317

%C .34.1028.13013.1041908..36816394..2322958629..154482346317...9172624830461

%C .55.2796.56318.7459468.431156277.49439157520.5662974500151.587385690244582

%H R. H. Hardin, <a href="/A299689/b299689.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

%F k=3: [order 15] for n>17

%F k=4: [order 44] for n>46

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A298148.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 16 2018