cp's OEIS Frontend

A222016 Number of nX3 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.

%I A222016 #6 Jul 23 2025 02:22:35
%S A222016 6,188,3875,86088,1892859,41636522,916164266,20156123913,443464985963,
%T A222016 9756801621038,214662580479904,4722860659023550,103909179716386461,
%U A222016 2286139384890550049,50298089904801491960,1106624498857041822230
%N A222016 Number of nX3 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.
%C A222016 Column 3 of A222020
%H A222016 R. H. Hardin, <a href="/A222016/b222016.txt">Table of n, a(n) for n = 1..195</a>
%F A222016 Empirical: a(n) = 6*a(n-1) +286*a(n-2) +1731*a(n-3) -3366*a(n-4) -58755*a(n-5) -73158*a(n-6) +744580*a(n-7) +1606773*a(n-8) -5847271*a(n-9) -13299665*a(n-10) +35585397*a(n-11) +56858689*a(n-12) -168213873*a(n-13) -99886051*a(n-14) +532060381*a(n-15) -127805646*a(n-16) -951724652*a(n-17) +874261131*a(n-18) +729065885*a(n-19) -1511277493*a(n-20) +275583551*a(n-21) +992093720*a(n-22) -708567632*a(n-23) -119679569*a(n-24) +310913349*a(n-25) -92576435*a(n-26) -25624476*a(n-27) +17876348*a(n-28) -1254086*a(n-29) -1085212*a(n-30) +391330*a(n-31) -46391*a(n-32) -25190*a(n-33) +7306*a(n-34) +873*a(n-35) -236*a(n-36) -12*a(n-37)
%e A222016 Some solutions for n=3
%e A222016 ..2..0..2....0..1..1....1..0..1....0..0..0....0..3..0....0..0..0....0..2..1
%e A222016 ..0..3..0....1..3..2....0..1..2....2..3..2....1..0..2....3..2..2....0..1..2
%e A222016 ..1..1..0....0..1..0....2..1..1....1..1..0....1..1..1....1..0..1....2..1..0
%K A222016 nonn
%O A222016 1,1
%A A222016 _R. H. Hardin_ Feb 05 2013