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%I #6 May 16 2023 15:47:54
%S 130,4580,67585,638996,4646480,28403642,153482649,753824187,
%T 3415377142,14392067725,56709869639,209870332819,732443566502,
%U 2420139228330,7599650363003,22760832153158,65233797272228,179466761579280
%N Number of n X 4 0..3 arrays with rows and columns unimodal and antidiagonals nondecreasing.
%C Column 4 of A224050.
%H R. H. Hardin, <a href="/A224046/b224046.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/2906843957821440000)*n^24 + (1/34605285212160000)*n^23 + (2197/1372406261022720000)*n^22 + (36671/608225502044160000)*n^21 + (345821/198604245565440000)*n^20 + (243821/6097498767360000)*n^19 + (2713831/3556874280960000)*n^18 + (65882659/5335311421440000)*n^17 + (1717274701/10042939146240000)*n^16 + (15328652863/7532204359680000)*n^15 + (310603695671/15064408719360000)*n^14 + (2357040641/12809871360000)*n^13 + (164927026281001/110472330608640000)*n^12 + (9207360567227/836911595520000)*n^11 + (4986853452139/64377815040000)*n^10 + (411697824533651/941525544960000)*n^9 + (65628631692258281/32011868528640000)*n^8 + (272989349985619/42343741440000)*n^7 + (2379724164506688719/152056375511040000)*n^6 + (12014199897579587/351982350720000)*n^5 + (1477480261274551/84475764172800)*n^4 + (999826201817147/5866372512000)*n^3 - (44639957516956097/148419224553600)*n^2 + (38158075159/56360304)*n - 1449 for n>3.
%e Some solutions for n=3
%e ..2..3..3..3....0..1..3..3....2..1..0..0....0..1..0..0....0..0..0..0
%e ..3..3..3..0....3..3..3..2....3..3..1..1....1..2..2..2....2..2..3..1
%e ..3..3..0..0....3..3..2..2....3..3..3..3....2..3..2..0....3..3..1..0
%Y Cf. A224050.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 01 2013
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