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

0,2

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

Links

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

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

Example

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

Crossrefs

Column 2 of A227165.

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

Sequence in context: A036628 A004035 A169763 * A241080 A366724 A332706

Adjacent sequences: A227158 A227159 A227160 * A227162 A227163 A227164

Keyword

nonn

Author

R. H. Hardin, Jul 03 2013

Extensions

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

Status

approved