cp's OEIS Frontend

A227161 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of one or less, with rows and columns of the latter in lexicographically nondecreasing order.

%I A227161 #23 Jan 24 2017 02:38:58
%S A227161 1,3,8,18,36,66,113,183,283,421,606,848,1158,1548,2031,2621,3333,4183,
%T A227161 5188,6366,7736,9318,11133,13203,15551,18201,21178,24508,28218,32336,
%U A227161 36891,41913,47433,53483,60096,67306,75148,83658,92873,102831,113571,125133
%N A227161 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of one or less, with rows and columns of the latter in lexicographically nondecreasing order.
%C A227161 Also number of binary words with 3 1's and at most n 0's that do not contain the substring 101. a(2) = 8: 111, 0111, 1110, 00111, 10011, 11001, 11100, 01110. - _Alois P. Heinz_, Jul 18 2013
%H A227161 R. H. Hardin, <a href="/A227161/b227161.txt">Table of n, a(n) for n = 0..210</a>
%F A227161 Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 + (23/24)*n^2 + (11/12)*n + 1.
%F A227161 G.f.: -(1-x+x^2)^2/(x-1)^5. - _Alois P. Heinz_, Jul 18 2013
%F A227161 Binomial transform of (1 + 2x + 3x^2 + 2x^3 + x^4), i.e., of (1 + x + x^2)^2. - _Gary W. Adamson_, Jan 23 2017
%e A227161 Some solutions for n=4:
%e A227161 ..1..0....1..1....1..1....0..0....1..0....1..0....1..0....1..1....1..1....1..1
%e A227161 ..0..0....1..1....1..1....0..0....0..0....1..0....1..0....1..1....1..0....1..0
%e A227161 ..0..1....1..1....1..0....0..0....0..1....1..0....1..0....1..0....0..0....1..0
%e A227161 ..0..0....1..0....0..0....0..1....0..1....1..0....0..0....0..1....0..0....0..0
%Y A227161 Column 2 of A227165.
%Y A227161 First differences give A177787. - _Alois P. Heinz_, Jul 18 2013
%K A227161 nonn
%O A227161 0,2
%A A227161 _R. H. Hardin_, Jul 03 2013
%E A227161 a(0) = 1 added by _Alois P. Heinz_, Jul 18 2013