A227122 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 zero, with rows and columns of the latter in lexicographically nondecreasing order.

4, 13, 33, 81, 202, 492, 1143, 2524, 5315, 10718, 20776, 38839, 70225, 123134, 209884, 348550, 565100, 896136, 1392363, 2122925, 3180764, 4689176, 6809757, 9751952, 13784441, 19248618, 26574442, 36298963, 49087851, 65760282, 87317562

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/362880)*n^9 + (31/60480)*n^7 + (13/17280)*n^5 + (5/12)*n^4 - (167659/90720)*n^3 + (43/12)*n^2 + (12407/1260)*n - 14 for n>2.

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

G.f.: x*(4 - 27*x + 83*x^2 - 144*x^3 + 157*x^4 - 121*x^5 + 87*x^6 - 62*x^7 + 28*x^8 - x^9 - 4*x^10 + x^11) / (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>12.

(End)

Example

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

Crossrefs

Column 3 of A227125

Sequence in context: A302082 A124669 A036894 * A176361 A322599 A135859

Adjacent sequences: A227119 A227120 A227121 * A227123 A227124 A227125

Keyword

nonn

Author

R. H. Hardin, Jul 01 2013

Status

approved