A227099 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 two, with rows and columns of the latter in lexicographically nondecreasing order.

4, 15, 48, 136, 341, 771, 1606, 3133, 5789, 10214, 17315, 28342, 44977, 69437, 104592, 154099, 222553, 315656, 440405, 605300, 820573, 1098439, 1453370, 1902393, 2465413, 3165562, 4029575, 5088194, 6376601, 7934881, 9808516, 12048911

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/5040)*n^7 + (1/240)*n^6 + (13/720)*n^5 + (5/48)*n^4 + (119/90)*n^3 - (73/120)*n^2 - (2873/420)*n + 23 for n>3.

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

G.f.: x*(4 - 17*x + 40*x^2 - 52*x^3 + 37*x^4 - 11*x^5 + 2*x^6 - 3*x^7 - x^8 + 3*x^9 - x^10) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>11.

(End)

Example

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

Crossrefs

Column 2 of A227103.

Sequence in context: A219903 A238807 A240333 * A225976 A093967 A052201

Adjacent sequences: A227096 A227097 A227098 * A227100 A227101 A227102

Keyword

nonn

Author

R. H. Hardin, Jul 01 2013

Status

approved