login
Number of 4 X n 0..1 arrays with every element equal to 0, 2, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
1

%I #6 May 03 2021 12:58:17

%S 8,2,8,2,12,10,46,50,204,290,1034,1682,5458,9802,29582,57122,163166,

%T 332930,911976,1940450,5149146,11309770,29300080,65918162,167721900,

%U 384199202,964447184,2239277042,5564863708,13051463050,32192084054

%N Number of 4 X n 0..1 arrays with every element equal to 0, 2, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Row 4 of A303325.

%H R. H. Hardin, <a href="/A303326/b303326.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +9*a(n-2) -16*a(n-3) -25*a(n-4) +34*a(n-5) +15*a(n-6) +4*a(n-7) +34*a(n-8) -64*a(n-9) -42*a(n-10) +20*a(n-11) -7*a(n-12) +34*a(n-13) +21*a(n-14) -8*a(n-15) -a(n-16) -6*a(n-17) -3*a(n-18) for n > 19.

%e Some solutions for n=5

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

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

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

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

%Y Cf. A303325.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 21 2018