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A224147 Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing. 1

%I

%S 4,16,49,124,275,554,1037,1831,3082,4984,7789,11818,17473,25250,35753,

%T 49709,67984,91600,121753,159832,207439,266410,338837,427091,533846,

%U 662104,815221,996934,1211389,1463170,1757329,2099417,2495516,2952272

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

%C Row 3 of A224146.

%H R. H. Hardin, <a href="/A224147/b224147.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/720)*n^6 + (1/80)*n^5 + (23/144)*n^4 + (29/48)*n^3 + (241/180)*n^2 + (53/60)*n + 1.

%F Conjectures from _Colin Barker_, Aug 28 2018: (Start)

%F G.f.: x*(4 - 12*x + 21*x^2 - 23*x^3 + 16*x^4 - 6*x^5 + x^6) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A224146.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 31 2013

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Last modified June 28 12:59 EDT 2022. Contains 354907 sequences. (Running on oeis4.)