A223616 - OEIS

%I #8 Aug 21 2018 10:16:33

%S 11,121,876,4466,17594,57238,160883,403159,921181,1951247,3879910,

%T 7312800,13164932,22776596,38059285,61676477,97264447,149698645,

%U 225411536,332768158,482506014,688246274,967083623,1340262451,1833947441

%N Number of n X 4 0..1 arrays with rows and columns unimodal.

%C Column 4 of A223620.

%H R. H. Hardin, <a href="/A223616/b223616.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/112)*n^8 + (79/1260)*n^7 + (59/180)*n^6 + (299/360)*n^5 + (259/144)*n^4 + (821/360)*n^3 + (7219/2520)*n^2 + (767/420)*n + 1.

%F Conjectures from _Colin Barker_, Aug 21 2018: (Start)

%F G.f.: x*(11 + 22*x + 183*x^2 + 14*x^3 + 158*x^4 - 56*x^5 + 35*x^6 - 8*x^7 + x^8) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A223620.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 24 2013