A281951 - OEIS

%I #6 Oct 19 2021 21:48:07

%S 8,112,587,3389,19089,111354,640778,3716432,21502354,124531091,

%T 721152740,4176107752,24184974414,140057032575,811098268642,

%U 4697197830808,27202297829372,157533202227607,912302039312046,5283299749392401

%N Number of n X 4 0..1 arrays with no element unequal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

%C Column 4 of A281955.

%H R. H. Hardin, <a href="/A281951/b281951.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +14*a(n-2) -45*a(n-3) -87*a(n-4) +179*a(n-5) +51*a(n-6) -197*a(n-7) +424*a(n-8) -224*a(n-9) -890*a(n-10) +887*a(n-11) +660*a(n-12) -788*a(n-13) -418*a(n-14) +178*a(n-15) +92*a(n-16) -27*a(n-17) +60*a(n-18) +69*a(n-19) +95*a(n-20) -a(n-21) -5*a(n-22) -45*a(n-23) -10*a(n-24) -9*a(n-25) -6*a(n-26) +3*a(n-28) for n > 32.

%e Some solutions for n=4

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

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

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

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

%Y Cf. A281955.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 03 2017