cp's OEIS Frontend

A208348 Number of nX3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

%I A208348 #7 Jun 02 2025 07:43:59
%S A208348 5,100,1095,12625,153237,1901508,23658861,294608660,3672171940,
%T A208348 45806539501,571496743787,7130666296577,88976864630029,
%U A208348 1110304369879641,13855224093424061,172897096309149243,2157565319312754303
%N A208348 Number of nX3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).
%C A208348 Column 3 of A208353
%H A208348 R. H. Hardin, <a href="/A208348/b208348.txt">Table of n, a(n) for n = 1..210</a>
%F A208348 Empirical: a(n) = 21*a(n-1) -90*a(n-2) -532*a(n-3) +5973*a(n-4) -31315*a(n-5) +73172*a(n-6) +692866*a(n-7) -5872588*a(n-8) +14338130*a(n-9) +13545534*a(n-10) -238643374*a(n-11) +1047870400*a(n-12) -1941550084*a(n-13) -2024947104*a(n-14) +17313536656*a(n-15) -33786142200*a(n-16) +21548688152*a(n-17) +32421829160*a(n-18) -107335908376*a(n-19) +165792590624*a(n-20) -118619608528*a(n-21) -73538891712*a(n-22) +207386497216*a(n-23) -223952516832*a(n-24) +322902169696*a(n-25) -245567709568*a(n-26) -217360125376*a(n-27) +464272398720*a(n-28) -172433924352*a(n-29) -145159584768*a(n-30) +86842756096*a(n-31) +128366311424*a(n-32) -108640727040*a(n-33) -53571584000*a(n-34) +74317824000*a(n-35) -18063360000*a(n-36) for n>39
%e A208348 Some solutions for n=4
%e A208348 ..0..0..0....0..1..2....0..0..1....0..0..0....0..1..0....0..1..1....0..0..0
%e A208348 ..1..0..2....3..0..1....0..2..1....1..1..1....1..2..2....2..3..2....1..0..1
%e A208348 ..3..1..2....2..1..0....2..2..1....2..1..2....3..2..2....3..2..3....2..2..2
%e A208348 ..1..3..1....1..0..1....3..2..0....3..2..0....1..3..0....1..1..1....1..2..3
%K A208348 nonn
%O A208348 1,1
%A A208348 _R. H. Hardin_ Feb 25 2012