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A223931 Number of nX6 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

%I A223931 #6 Jul 23 2025 04:39:57
%S A223931 148,4690,49646,316136,1548633,6621074,26250443,98910688,356869229,
%T A223931 1233491661,4078987936,12893958739,38971222534,112766372283,
%U A223931 313016886779,835552379045,2150549167905,5351315229801,12907390753903,30251757926890
%N A223931 Number of nX6 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.
%C A223931 Column 6 of A223933
%H A223931 R. H. Hardin, <a href="/A223931/b223931.txt">Table of n, a(n) for n = 1..141</a>
%F A223931 Empirical: a(n) = (1/35608838483312640000)*n^24 - (1/989134402314240000)*n^23 + (1/12843374100480000)*n^22 - (6449/4257578514309120000)*n^21 + (21257/304112751022080000)*n^20 - (829363/1216451004088320000)*n^19 + (40421209/896332318801920000)*n^18 - (9123221/16598746644480000)*n^17 + (633266813/17575143505920000)*n^16 - (337664083/599152619520000)*n^15 + (2727091523/144850083840000)*n^14 - (437501744297/941525544960000)*n^13 + (331492439551297/26362715258880000)*n^12 - (779880875442583/2929190584320000)*n^11 + (6466629168070943/1351934115840000)*n^10 - (1887207111269150711/26362715258880000)*n^9 + (1852948610513538961/2000741783040000)*n^8 - (82282526794806272279/8002967132160000)*n^7 + (671840992562382243287/6956827637760000)*n^6 - (3984160216854431049887/5375730447360000)*n^5 + (4404199128820894274957/985550582016000)*n^4 - (7353970133174044661/365018734080)*n^3 + (398286504848891623/6290282880)*n^2 - (651587469103938359/5354228880)*n + 102401506 for n>12
%e A223931 Some solutions for n=3
%e A223931 ..0..0..0..0..0..0....0..2..1..1..1..0....0..0..0..0..0..0....0..0..2..0..0..0
%e A223931 ..0..1..1..0..0..0....0..2..2..2..2..2....0..1..1..1..1..1....0..1..2..2..0..0
%e A223931 ..0..1..1..1..2..2....0..0..2..2..2..2....0..2..2..1..1..1....0..1..1..2..2..0
%K A223931 nonn
%O A223931 1,1
%A A223931 _R. H. Hardin_ Mar 29 2013