cp's OEIS Frontend

A207107 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207107 #9 Feb 20 2018 14:27:59
%S A207107 9,81,271,643,1271,2239,3641,5581,8173,11541,15819,21151,27691,35603,
%T A207107 45061,56249,69361,84601,102183,122331,145279,171271,200561,233413,
%U A207107 270101,310909,356131,406071,461043,521371,587389,659441,737881,823073
%N A207107 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207107 Column 4 of A207111.
%H A207107 R. H. Hardin, <a href="/A207107/b207107.txt">Table of n, a(n) for n = 1..210</a>
%F A207107 Empirical: a(n) = (5/12)*n^4 + (13/2)*n^3 + (115/12)*n^2 - (17/2)*n + 1.
%F A207107 Conjectures from _Colin Barker_, Feb 20 2018: (Start)
%F A207107 G.f.: x*(9 + 36*x - 44*x^2 + 8*x^3 + x^4) / (1 - x)^5.
%F A207107 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A207107 (End)
%e A207107 Some solutions for n=4:
%e A207107 ..1..1..1..1....1..0..0..1....0..0..1..0....1..0..0..1....0..1..0..0
%e A207107 ..1..1..1..1....1..0..0..1....1..0..0..1....0..1..0..0....0..0..1..0
%e A207107 ..1..1..1..1....1..0..0..1....0..0..1..0....0..1..0..1....0..0..1..0
%e A207107 ..1..1..1..1....1..0..0..1....1..0..1..0....0..1..0..0....0..0..1..0
%Y A207107 Cf. A207111.
%K A207107 nonn
%O A207107 1,1
%A A207107 _R. H. Hardin_, Feb 15 2012