A227266 Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having a sum of three or less, with rows and columns of the latter in lexicographically nondecreasing order.

4, 16, 49, 132, 341, 836, 1934, 4232, 8804, 17501, 33392, 61393, 109141, 188181, 315546, 515823, 823812, 1287900, 1974288, 2972226, 4400429, 6414866, 9218134, 13070650, 18303916, 25336135, 34690480, 47016343, 63113917, 83962491

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/362880)*n^9 + (1/40320)*n^8 + (5/12096)*n^7 + (19/2880)*n^6 - (611/17280)*n^5 + (3407/5760)*n^4 - (5281/9072)*n^3 - (66509/10080)*n^2 + (22991/504)*n - 59 for n>3.

Conjectures from Colin Barker, Sep 07 2018: (Start)

G.f.: x*(4 - 24*x + 69*x^2 - 118*x^3 + 146*x^4 - 162*x^5 + 177*x^6 - 156*x^7 + 90*x^8 - 31*x^9 + 9*x^10 - 4*x^11 + x^12) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>13.

(End)

Example

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

Crossrefs

Column 3 of A227269.

Sequence in context: A237986 A086601 A224147 * A114185 A188516 A188501

Adjacent sequences: A227263 A227264 A227265 * A227267 A227268 A227269

Keyword

nonn

Author

R. H. Hardin, Jul 04 2013

Status

approved