cp's OEIS Frontend

A227021 Number of n X 2 (0,1,2) arrays of permanents of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.

%I A227021 #7 Sep 06 2018 11:30:19
%S A227021 7,26,72,171,368,729,1343,2325,3819,6001,9082,13311,18978,26417,36009,
%T A227021 48185,63429,82281,105340,133267,166788,206697,253859,309213,373775,
%U A227021 448641,534990,634087,747286,876033,1021869,1186433,1371465,1578809
%N A227021 Number of n X 2 (0,1,2) arrays of permanents of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
%H A227021 R. H. Hardin, <a href="/A227021/b227021.txt">Table of n, a(n) for n = 1..210</a>
%F A227021 Empirical: a(n) = (1/40)*n^5 + (1/3)*n^4 - (1/8)*n^3 + (5/3)*n^2 + (141/10)*n - 15 for n>2.
%F A227021 Conjectures from _Colin Barker_, Sep 06 2018: (Start)
%F A227021 G.f.: x*(7 - 16*x + 21*x^2 - 11*x^3 + 7*x^4 - 6*x^5 + x^7) / (1 - x)^6.
%F A227021 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A227021 (End)
%e A227021 Some solutions for n=4:
%e A227021 ..0..0....0..0....0..1....1..2....0..1....0..0....0..1....0..0....0..0....1..1
%e A227021 ..0..1....0..1....0..0....2..2....0..0....0..0....1..0....0..2....1..1....1..1
%e A227021 ..2..1....0..0....0..0....2..2....1..0....1..2....1..0....0..2....0..0....2..1
%e A227021 ..2..2....1..1....1..0....2..2....0..0....2..2....2..0....0..2....0..0....2..2
%Y A227021 Column 2 of A227025.
%K A227021 nonn
%O A227021 1,1
%A A227021 _R. H. Hardin_, Jun 27 2013