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Number of n X 5 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
1

%I #7 Aug 23 2018 16:52:04

%S 16,86,255,596,1240,2388,4325,7436,12222,19316,29499,43716,63092,

%T 88948,122817,166460,221882,291348,377399,482868,610896,764948,948829,

%U 1166700,1423094,1722932,2071539,2474660,2938476,3469620,4075193,4762780,5540466

%N Number of n X 5 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%C Column 5 of A223838.

%H R. H. Hardin, <a href="/A223835/b223835.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (2/15)*n^5 + (1/6)*n^4 + (19/6)*n^3 + (28/3)*n^2 + (126/5)*n - 36 for n>2.

%F Conjectures from _Colin Barker_, Aug 23 2018: (Start)

%F G.f.: x*(16 - 10*x - 21*x^2 + 36*x^3 + 9*x^4 - 18*x^5 + 2*x^6 + 2*x^7) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>8.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A223838.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 27 2013