A300141 - OEIS

A300141

Number of nX3 0..1 arrays with every element equal to 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%I #4 Feb 26 2018 08:08:02

%S 0,4,1,18,41,130,510,1740,5554,20089,69607,233844,815086,2824883,

%T 9656170,33351986,115270625,396350451,1366335435,4714673357,

%U 16240450509,55971672188,193001422391,665159525391,2292527902957,7903063069976

%N Number of nX3 0..1 arrays with every element equal to 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A300146.

%H R. H. Hardin, <a href="/A300141/b300141.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +3*a(n-2) +18*a(n-3) -21*a(n-4) -54*a(n-5) -54*a(n-6) +79*a(n-7) +119*a(n-8) +4*a(n-9) -3*a(n-10) -a(n-11) +26*a(n-12) -53*a(n-13) -17*a(n-14) +15*a(n-15) for n>17

%e Some solutions for n=5

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

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

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

%Y Cf. A300146.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 26 2018