login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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

%I #6 Jul 29 2022 22:08:02

%S 1,2,2,4,11,26,76,222,721,2361,7737,25780,85449,284610,947298,3154457,

%T 10507280,34994885,116569493,388281532,1293363746,4308190293,

%U 14350558511,47801810756,159227933912,530389181794,1766729082040,5884984209038

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

%C Column 4 of A298782.

%H R. H. Hardin, <a href="/A298778/b298778.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +5*a(n-2) -8*a(n-3) -21*a(n-4) +8*a(n-5) +16*a(n-6) +19*a(n-7) +5*a(n-8) +10*a(n-9) -12*a(n-10) -43*a(n-11) -12*a(n-12) -3*a(n-13) +26*a(n-14) +11*a(n-15) +7*a(n-16) -3*a(n-17) -13*a(n-18) +7*a(n-19) +2*a(n-20) -3*a(n-21) for n>27.

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A298782.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 26 2018