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.

1, 3, 8, 18, 36, 66, 113, 183, 283, 421, 606, 848, 1158, 1548, 2031, 2621, 3333, 4183, 5188, 6366, 7736, 9318, 11133, 13203, 15551, 18201, 21178, 24508, 28218, 32336, 36891, 41913, 47433, 53483, 60096, 67306, 75148, 83658, 92873, 102831, 113571, 125133

Offset: 0

Author

R. H. Hardin, Jul 03 2013

Keywords

• nonn

Comments

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

Examples

			Some solutions for n=4:
..1..0....1..1....1..1....0..0....1..0....1..0....1..0....1..1....1..1....1..1
..0..0....1..1....1..1....0..0....0..0....1..0....1..0....1..1....1..0....1..0
..0..1....1..1....1..0....0..0....0..1....1..0....1..0....1..0....0..0....1..0
..0..0....1..0....0..0....0..1....0..1....1..0....0..0....0..1....0..0....0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 0..210

Crossrefs

Column 2 of A227165.

First differences give A177787. - Alois P. Heinz, Jul 18 2013

Formula

Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 + (23/24)*n^2 + (11/12)*n + 1.

G.f.: -(1-x+x^2)^2/(x-1)^5. - Alois P. Heinz, Jul 18 2013

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

Extensions

a(0) = 1 added by Alois P. Heinz, Jul 18 2013