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A241331 Number of 4Xn 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

%I A241331 #6 Jul 23 2025 11:12:49
%S A241331 15,1030,95144,8949808,842185933,79254376889,7458275852500,
%T A241331 701865426977495,66049458199029896,6215623102818695436,
%U A241331 584924867215713568482,55044698604373555829472,5180013732180082600538625
%N A241331 Number of 4Xn 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.
%C A241331 Row 4 of A241328
%H A241331 R. H. Hardin, <a href="/A241331/b241331.txt">Table of n, a(n) for n = 1..210</a>
%F A241331 Empirical: a(n) = 122*a(n-1) -2812*a(n-2) +16208*a(n-3) +159379*a(n-4) -2909948*a(n-5) +19694228*a(n-6) -62373244*a(n-7) -58088806*a(n-8) +1439148868*a(n-9) -5096351523*a(n-10) -3055067884*a(n-11) +59968811184*a(n-12) -73039493422*a(n-13) -301989142269*a(n-14) +945040962120*a(n-15) -745735386949*a(n-16) -844626880720*a(n-17) +2521153036681*a(n-18) -1929013979294*a(n-19) -1045472186222*a(n-20) +1583296164696*a(n-21) +1956836924036*a(n-22) -2355373350354*a(n-23) -3690081020076*a(n-24) +7567309408680*a(n-25) -2089000784295*a(n-26) -4919238685854*a(n-27) +4312880045136*a(n-28) -566304913242*a(n-29) -920941508979*a(n-30) +911638855890*a(n-31) -424728198324*a(n-32) -322761834*a(n-33) +96291263349*a(n-34) -53052692148*a(n-35) +11321287623*a(n-36) for n>38
%e A241331 Some solutions for n=3
%e A241331 ..0..1..2....0..1..2....0..1..2....0..1..0....0..1..2....0..1..2....0..1..2
%e A241331 ..0..1..0....0..2..0....1..0..2....2..3..2....2..0..1....3..0..1....3..2..1
%e A241331 ..1..0..1....0..1..2....0..3..0....1..2..0....1..3..1....2..3..2....1..0..3
%e A241331 ..0..2..1....3..2..1....3..0..1....2..1..0....3..0..2....3..1..0....3..2..0
%K A241331 nonn
%O A241331 1,1
%A A241331 _R. H. Hardin_, Apr 19 2014