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A224025 Number of 3 X n 0..3 arrays with rows nondecreasing and antidiagonals unimodal. 1

%I

%S 64,1000,6796,32523,122523,387729,1074167,2679260,6137666,13104218,

%T 26368076,50439449,92358199,162782299,277423483,458907498,739147146,

%U 1162327788,1788617172,2698724343,3999445995,5830352933,8371784327

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

%C Row 3 of A224024.

%H R. H. Hardin, <a href="/A224025/b224025.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (353/181440)*n^9 + (5/126)*n^8 + (12287/30240)*n^7 + (131/60)*n^6 + (64877/8640)*n^5 + (135/8)*n^4 + (998257/45360)*n^3 + (53933/2520)*n^2 + (3421/252)*n - 2 for n>1.

%F Conjectures from _Colin Barker_, Aug 26 2018: (Start)

%F G.f.: x*(64 + 360*x - 324*x^2 + 1883*x^3 - 3447*x^4 + 4386*x^5 - 3748*x^6 + 2193*x^7 - 825*x^8 + 182*x^9 - 18*x^10) / (1 - x)^10.

%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>11.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A224024.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 30 2013

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Last modified November 20 17:09 EST 2019. Contains 329337 sequences. (Running on oeis4.)