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A224174 Number of 3 X n 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing. 1

%I

%S 20,400,4739,38561,242114,1253770,5588411,22075529,78911656,259222964,

%T 791787532,2269535600,6149706181,15847969147,39036356744,92295124070,

%U 210220319550,462719488690,986952548003,2044823738533,4124042889158

%N Number of 3 X n 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%C Row 3 of A224173.

%H R. H. Hardin, <a href="/A224174/b224174.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/3629463552000)*n^18 + (1/80654745600)*n^17 + (5153/10461394944000)*n^16 + (33323/2615348736000)*n^15 + (186871/747242496000)*n^14 + (566921/149448499200)*n^13 + (390989/8211456000)*n^12 + (13776731/28740096000)*n^11 + (283859867/73156608000)*n^10 + (359930911/14631321600)*n^9 + (13824123559/114960384000)*n^8 + (6442744127/14370048000)*n^7 + (11719345643/8895744000)*n^6 + (10048449577/3736212480)*n^5 + (1016995336979/217945728000)*n^4 + (32943067909/9081072000)*n^3 + (5801778061/735134400)*n^2 - (393478/36465)*n + 10.

%e Some solutions for n=3

%e ..1..1..1....2..1..0....1..1..0....0..0..1....1..1..0....0..1..2....0..3..1

%e ..2..2..1....2..1..1....1..1..0....2..3..1....1..2..0....1..2..3....2..3..1

%e ..2..2..3....2..1..1....1..2..3....3..3..1....1..3..3....1..2..3....2..3..2

%Y Cf. A224173.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 31 2013

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Last modified May 26 03:55 EDT 2022. Contains 354074 sequences. (Running on oeis4.)