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A209043 Number of nX4 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.

%I A209043 #7 Jul 22 2025 21:35:45
%S A209043 108,13644,1752148,225262148,28964458546,3724317998214,
%T A209043 478881915072688,61575811582924326,7917568966250856112,
%U A209043 1018060448767393518568,130904710995247416149996,16832049002507023710858048
%N A209043 Number of nX4 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.
%C A209043 Column 4 of A209047
%H A209043 R. H. Hardin, <a href="/A209043/b209043.txt">Table of n, a(n) for n = 1..210</a>
%F A209043 Empirical: a(n) = 81*a(n-1) +6019*a(n-2) +17676*a(n-3) -599593*a(n-4) -4088888*a(n-5) -3730999*a(n-6) +101900822*a(n-7) +392580866*a(n-8) -1523969122*a(n-9) -1305957528*a(n-10) +28806814857*a(n-11) -138610167727*a(n-12) -92479090429*a(n-13) +1908411722538*a(n-14) -4688061743329*a(n-15) +868176994167*a(n-16) +37238901400055*a(n-17) -108429686426996*a(n-18) +63224602311532*a(n-19) +146638886828725*a(n-20) -399120237191674*a(n-21) +643043970497948*a(n-22) +657212030688884*a(n-23) -3350737459002767*a(n-24) -512333788345638*a(n-25) +9658795596391494*a(n-26) -7307540288812320*a(n-27) +4046894684677414*a(n-28) -49280938427249*a(n-29) -15919719904208233*a(n-30) +5309011068556252*a(n-31) -27520223522274361*a(n-32) -15861006441701489*a(n-33) +40304491599363659*a(n-34) +82471636953173637*a(n-35) +47893641143347577*a(n-36) -40160830349734528*a(n-37) -42797055661074986*a(n-38) -77937400975405899*a(n-39) -41530998228072484*a(n-40) +13888895933404573*a(n-41) +29183625221012494*a(n-42) +57292324471563068*a(n-43) +24864119964192191*a(n-44) -8835195495823362*a(n-45) -12319214526059338*a(n-46) -1662673048234914*a(n-47) +3583743936817358*a(n-48) -188032462140047*a(n-49) -184935511247693*a(n-50) +57632509822517*a(n-51) +92193118733688*a(n-52) -31500301490757*a(n-53) +6805810881792*a(n-54) +8054118978759*a(n-55) +514316253699*a(n-56) -51314595768*a(n-57) +41840052498*a(n-58) +7462586376*a(n-59) +4099260312*a(n-60) -90167823*a(n-61) -35429400*a(n-62) +1062882*a(n-63)
%e A209043 Some solutions for n=4
%e A209043 ..1..3..2..1....3..1..2..3....2..3..1..3....2..0..1..0....0..1..0..3
%e A209043 ..2..2..1..2....0..1..0..0....3..2..1..1....3..0..1..2....2..2..2..2
%e A209043 ..0..2..0..3....1..0..3..0....0..2..0..1....1..3..0..0....1..1..3..2
%e A209043 ..1..0..2..1....2..2..2..0....1..3..3..1....2..3..2..2....0..3..0..0
%K A209043 nonn
%O A209043 1,1
%A A209043 _R. H. Hardin_ Mar 04 2012