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A224378 Number of 6Xn 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

%I A224378 #6 Jul 23 2025 05:08:08
%S A224378 729,69984,1126072,8297747,42132769,174854516,644368221,2212959866,
%T A224378 7296488462,23473954511,74124038709,229565868000,694675751863,
%U A224378 2045339262040,5840640774160,16145608364197,43177424328109
%N A224378 Number of 6Xn 0..2 arrays with rows unimodal and antidiagonals nondecreasing.
%C A224378 Row 6 of A224374
%H A224378 R. H. Hardin, <a href="/A224378/b224378.txt">Table of n, a(n) for n = 1..210</a>
%F A224378 Empirical: a(n) = (1/35608838483312640000)*n^24 + (1/228261785149440000)*n^23 + (2993/8515157028618240000)*n^22 + (1189/64508765368320000)*n^21 + (565139/810967336058880000)*n^20 + (50213/2502985605120000)*n^19 + (102275011/224083079700480000)*n^18 + (630450937/74694359900160000)*n^17 + (6860509793/52725430517760000)*n^16 + (7572768857/4393785876480000)*n^15 + (1975549547/96566722560000)*n^14 + (5979889787/26153487360000)*n^13 + (129750858133763/52725430517760000)*n^12 + (8852225741519/337983528960000)*n^11 + (1757155928198569/6590678814720000)*n^10 + (11208897154284701/4393785876480000)*n^9 + (15905213251807771/762187345920000)*n^8 + (60693804091491173/444609285120000)*n^7 + (56813409423945822743/88699552381440000)*n^6 + (45278410760324474101/29566517460480000)*n^5 - (4851359450955021973/4927752910080000)*n^4 - (59510428654061699/5133075948000)*n^3 + (926682017129053/38440617600)*n^2 + (89190882279703/5354228880)*n - 49724 for n>4
%e A224378 Some solutions for n=3
%e A224378 ..0..0..1....0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..0
%e A224378 ..0..1..0....0..0..2....1..1..0....1..0..0....1..0..0....0..1..0....0..0..0
%e A224378 ..2..2..0....0..2..0....1..0..0....0..2..1....2..2..2....2..2..0....2..1..0
%e A224378 ..2..0..0....2..0..0....2..0..0....2..2..1....2..2..0....2..0..0....1..1..2
%e A224378 ..2..1..1....1..0..0....0..2..2....2..2..1....2..2..0....1..0..0....1..2..0
%e A224378 ..2..1..0....0..1..0....2..2..0....2..2..1....2..2..2....2..1..0....2..1..0
%K A224378 nonn
%O A224378 1,1
%A A224378 _R. H. Hardin_ Apr 05 2013