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A252928 Number of nX6 nonnegative integer arrays with upper left 0 and lower right n+6-6 and value increasing by 0 or 1 with every step right or down.

%I A252928 #6 Jul 23 2025 13:46:23
%S A252928 5,120,2859,53950,762227,8241540,71297441,512868867,3160111147,
%T A252928 17063990547,82211677028,358529577294,1432148475494,5291678799968,
%U A252928 18236349617760,59031011794076,180569195179185,524679580969208
%N A252928 Number of nX6 nonnegative integer arrays with upper left 0 and lower right n+6-6 and value increasing by 0 or 1 with every step right or down.
%C A252928 Column 6 of A252930
%H A252928 R. H. Hardin, <a href="/A252928/b252928.txt">Table of n, a(n) for n = 1..210</a>
%F A252928 Empirical: a(n) = (331/583128197117706240000)*n^24 + (331/3738001263575040000)*n^23 + (31687/5070679974936576000)*n^22 + (9719/36584992604160000)*n^21 + (83457079/10948059036794880000)*n^20 + (2293999511/14597412049059840000)*n^19 + (70133801/28810681675776000)*n^18 + (11352513167/384142422343680000)*n^17 + (39752887/135444234240000)*n^16 + (18525490537/7532204359680000)*n^15 + (1041895258531/59655058528665600)*n^14 + (51595236448757/497125487738880000)*n^13 + (383722831905761/745688231608320000)*n^12 + (7387354289669/3476402012160000)*n^11 + (96126694933271/13557967847424000)*n^10 + (3074811780539/156920924160000)*n^9 + (7254553057678669/144053408378880000)*n^8 + (5122046760654749/48017802792960000)*n^7 + (615467828621/1796401152000)*n^6 + (481180027609747/666913927680000)*n^5 + (6796574742313/5225109120000)*n^4 + (10424925937303/10188962784000)*n^3 - (3393867242681/1060137318240)*n^2 + (7032359801/2677114440)*n + 2
%e A252928 Some solutions for n=4
%e A252928 ..0..1..1..2..3..3....0..1..2..3..3..4....0..1..1..1..1..2....0..1..2..2..2..3
%e A252928 ..1..2..2..2..3..3....1..2..2..3..4..4....1..1..1..1..1..2....1..1..2..2..3..4
%e A252928 ..2..3..3..3..4..4....2..3..3..3..4..4....1..1..2..2..2..3....1..1..2..3..3..4
%e A252928 ..2..3..3..3..4..4....2..3..3..3..4..4....2..2..2..2..3..4....1..2..3..3..4..4
%K A252928 nonn
%O A252928 1,1
%A A252928 _R. H. Hardin_, Dec 24 2014