A227675 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having an odd sum, with rows and columns of the latter in lexicographically nondecreasing order.

4, 16, 50, 131, 301, 625, 1198, 2153, 3670, 5986, 9406, 14315, 21191, 30619, 43306, 60097, 81992, 110164, 145978, 191011, 247073, 316229, 400822, 503497, 627226, 775334, 951526, 1159915, 1405051, 1691951, 2026130, 2413633, 2861068, 3375640

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/720)*n^6 + (1/48)*n^5 + (29/144)*n^4 + (5/16)*n^3 + (647/360)*n^2 + (2/3)*n + 1.

Conjectures from Colin Barker, Sep 09 2018: (Start)

G.f.: x*(4 - 12*x + 22*x^2 - 23*x^3 + 14*x^4 - 5*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Column 2 of A227679.

Sequence in context: A217951 A217950 A217949 * A345325 A203094 A298173

Adjacent sequences: A227672 A227673 A227674 * A227676 A227677 A227678

Keyword

nonn

Author

R. H. Hardin, Jul 19 2013

Status

approved