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A202810 Number of nX6 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

%I A202810 #7 Jun 02 2025 07:28:44
%S A202810 1,21,881,43483,1874539,60758779,1420586923,24496279000,324818660255,
%T A202810 3450301922085,30392148400009,228299392737693,1495681511952100,
%U A202810 8702151387743758,45631559860107036,218282278670309658
%N A202810 Number of nX6 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.
%C A202810 Column 6 of A202812
%H A202810 R. H. Hardin, <a href="/A202810/b202810.txt">Table of n, a(n) for n = 1..210</a>
%F A202810 Empirical: a(n) = (1277297393/8289151869130970582384640000000)*n^30 + (1277297393/61401124956525708017664000000)*n^29 + (297094789/218819386084962100838400000)*n^28 + (7816341527/139600890389978873856000000)*n^27 + (3679424300173/2268514468837156700160000000)*n^26 + (215648816287/6204484017332394393600000)*n^25 + (132644124511021/234529495855164508078080000)*n^24 + (8516618187653/1206427447814632243200000)*n^23 + (452342167635389/6708509606841090048000000)*n^22 + (35730373202707/73570956727261593600000)*n^21 + (1251259179315059/485568314399926517760000)*n^20 + (1361341525505047/134880087333312921600000)*n^19 + (145094222851897967/3964119313133371392000000)*n^18 + (268476765510956759/1292009257613839564800000)*n^17 + (559775202052160947/410402940653807861760000)*n^16 + (455829405206713/78297264318873600000)*n^15 + (51349681364745987967/4152886899473055744000000)*n^14 + (321563032543235723/14197903929822412800000)*n^13 + (893790815923908266251/3823850475899421327360000)*n^12 + (151050517333396775323/128749174272707788800000)*n^11 + (1383273494122866878269/1572306939103380480000000)*n^10 - (3754718962122134858933/758700491249885184000000)*n^9 + (222617923041595086359/13219781286929817600000)*n^8 + (4614812385253095736069/53858368206010368000000)*n^7 - (647903194163313269910577/9189584075150519040000000)*n^6 - (1229353439820407340721/20421297944778931200000)*n^5 + (158913710606056931851/161220773248254720000)*n^4 - (11747119919207627/13357730209824000)*n^3 - (29007604104881443/31085582031504000)*n^2 + (443720625949/155272637520)*n - 1
%e A202810 Some solutions for n=4
%e A202810 ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
%e A202810 ..0..0..0..0..2..2....0..0..1..1..2..2....0..0..0..0..0..1....0..0..0..0..2..2
%e A202810 ..0..0..1..2..3..3....0..1..1..2..2..2....0..1..2..2..2..2....0..0..1..2..2..4
%e A202810 ..0..2..2..3..4..4....0..2..3..4..4..4....0..1..2..3..3..4....0..1..2..2..4..5
%K A202810 nonn
%O A202810 1,2
%A A202810 _R. H. Hardin_ Dec 24 2011