A223670 - OEIS

%I #7 Mar 16 2018 07:30:11

%S 8,64,292,948,2527,5913,12577,24821,46068,81198,136930,222250,348885,

%T 531823,789879,1146307,1629458,2273484,3119088,4214320,5615419,

%U 7387701,9606493,12358113,15740896,19866266,24859854,30862662,38032273,46544107

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

%C Row 3 of A223669.

%H R. H. Hardin, <a href="/A223670/b223670.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (23/360)*n^6 - (3/40)*n^5 + (37/18)*n^4 + (119/24)*n^3 - (3103/360)*n^2 + (997/60)*n - 9 for n>1.

%F Conjectures from _Colin Barker_, Mar 16 2018: (Start)

%F G.f.: x*(8 + 8*x + 12*x^2 - 32*x^3 + 63*x^4 - 16*x^5 + 5*x^6 - 2*x^7) / (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>8.

%F (End)

%e Some solutions for n=4:

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

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

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

%Y Cf. A223669.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 25 2013