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Number of n X 3 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.
1

%I #6 Apr 26 2021 19:13:58

%S 22,218,1586,11361,82700,615481,4634768,35003328,264487714,1997888432,

%T 15087449584,113921725004,860155842566,6494472790364,49035576285772,

%U 370236844834368,2795429838028120,21106576528056696,159362840727871756

%N Number of n X 3 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

%C Column 3 of A224310.

%H R. H. Hardin, <a href="/A224305/b224305.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) -16*a(n-2) -24*a(n-3) -44*a(n-4) +728*a(n-5) -678*a(n-6) -722*a(n-7) -860*a(n-8) +9336*a(n-9) -3916*a(n-10) +792*a(n-11) +320*a(n-12) -11936*a(n-13) +2848*a(n-14) +128*a(n-15) +384*a(n-16) +3840*a(n-17).

%e Some solutions for n=3

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

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

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

%Y Cf. A224310.

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 03 2013