A223681 - OEIS

%I #8 Aug 22 2018 06:25:17

%S 8,64,316,1118,3177,7745,16857,33615,62518,109838,184042,296260,

%T 460799,695703,1023359,1471149,2072148,2865868,3899048,5226490,

%U 6911941,9029021,11662197,14907803,18875106,23687418,29483254,36417536,44662843,54410707

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

%C Row 3 of A223680.

%H R. H. Hardin, <a href="/A223681/b223681.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (23/360)*n^6 + (31/120)*n^5 + (17/9)*n^4 + (23/24)*n^3 + (917/360)*n^2 + (77/60)*n + 1.

%F Conjectures from _Colin Barker_, Aug 22 2018: (Start)

%F G.f.: x*(8 + 8*x + 36*x^2 - 30*x^3 + 27*x^4 - 4*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 ..1..1..1....0..0..0....0..0..0....1..1..0....1..0..0....1..1..0....0..1..1

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

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

%Y Cf. A223680.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 25 2013