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%I #4 Mar 30 2013 11:10:42
%S 148,4690,57911,428949,2392915,11231300,46853641,179545949,646161612,
%T 2215310269,7295294696,23173431000,71137228340,211216789027,
%U 606907100518,1688654512840,4553248388246,11908977568334,30245780813181
%N Number of nX6 0..2 arrays with rows and columns unimodal and antidiagonals nondecreasing
%C Column 6 of A224057
%H R. H. Hardin, <a href="/A224055/b224055.txt">Table of n, a(n) for n = 1..178</a>
%F Empirical: a(n) = (1/35608838483312640000)*n^24 + (1/593480641388544000)*n^23 + (1/11491439984640000)*n^22 + (59/20274183401472000)*n^21 + (204271/2432902008176640000)*n^20 + (34451/17377871486976000)*n^19 + (18917939/448166159400960000)*n^18 + (769849/995924798668800)*n^17 + (226679623/17575143505920000)*n^16 + (2152013/11412430848000)*n^15 + (706815667/289700167680000)*n^14 + (9710969/517321728000)*n^13 + (22058018740169/52725430517760000)*n^12 + (883262112781/878757175296000)*n^11 + (30292372315283/675967057920000)*n^10 + (425362282393/5977939968000)*n^9 + (18858448588311589/8002967132160000)*n^8 - (2707211596157/114328101888000)*n^7 + (2638894624680309119/59133034920960000)*n^6 - (590269621381831/6636704256000)*n^5 + (21039414018476657/25935541632000)*n^4 - (10575054526365457/1955457504000)*n^3 + (4363361309424841/172982779200)*n^2 + (520015184729/102965940)*n - 216272 for n>7
%e Some solutions for n=3
%e ..1..0..0..0..0..0....0..0..0..0..2..0....0..1..1..0..0..0....0..0..0..0..2..0
%e ..2..0..0..0..0..0....0..0..1..2..1..0....1..2..2..0..0..0....0..0..2..2..1..0
%e ..1..1..0..0..0..0....0..2..2..1..1..1....2..2..2..1..1..0....2..2..2..1..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Mar 30 2013
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