%I #5 Mar 31 2012 12:36:45

%S 20,631,19827,499474,9603489,144262866,1757594146,17915547783,

%T 156619023957,1198133817532,8153980411514,50035648469991,

%U 279906963092730,1440489290975090,6871449852708897,30577097006475471,127620952939695332

%N Number of nX3 0..4 arrays with rows and columns lexicographically nondecreasing and no element equal to the number of horizontal and vertical neighbors equal to itself

%C Column 3 of A201729

%H R. H. Hardin, <a href="/A201724/b201724.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1143/13339406848768000000)*n^27 + (34659/3334851712192000000)*n^26 - (305829/102610821913600000)*n^25 + (18786617/246265972592640000)*n^24 + (3958894117/102610821913600000)*n^23 - (890060916037/160608242995200000)*n^22 + (3883955751623/13140674426880000)*n^21 + (15789034554253/1946766581760000)*n^20 - (43341713819681471/15162316646400000)*n^19 + (11737791620928206489/41496866611200000)*n^18 - (9354946607145085039/507183925248000)*n^17 + (89620729802927851309/99447828480000)*n^16 - (743803233665752540021073/21816367372800000)*n^15 + (28499385666924665391563347/29088489830400000)*n^14 - (25455135268631407928105381/1342545684480000)*n^13 + (461140646483326049588504801/5370182737920000)*n^12 + (28265806624709228060073236461/2593554163200000)*n^11 - (22551750300604775835503572048823/41496866611200000)*n^10 + (90452907504811296149083077682639/5631717611520000)*n^9 - (3032483358174968127916184659794719/8760449617920000)*n^8 + (393637850170773012106697103526188929/69493951296000000)*n^7 - (7869653987787486349645970604178160087/112927670856000000)*n^6 + (1901252628397296031171310111143845105449/3116803715625600000)*n^5 - (796590434152973474143064866658414914883/249344297250048000)*n^4 + (22209548841602923195409813138654672819/15006832704864000)*n^3 + (75783682547020727035019319582699319129/643149973065600)*n^2 - (1510369517764017479305249768151297/1784742960)*n + 2129912253933134417390679 for n>45

%e Some solutions for n=3

%e ..1..2..4....1..3..4....0..0..1....0..1..3....0..0..4....1..3..4....0..0..1

%e ..2..2..2....3..1..4....1..3..3....0..2..3....0..4..4....2..1..1....1..3..4

%e ..3..0..0....4..2..3....4..1..4....2..3..3....3..2..2....2..1..1....2..4..2

%K nonn

%O 1,1

%A _R. H. Hardin_ Dec 04 2011