A227162 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 one or less, with rows and columns of the latter in lexicographically nondecreasing order.

4, 18, 62, 193, 558, 1507, 3828, 9149, 20609, 43918, 88960, 172130, 319637, 572050, 990413, 1664308, 2722302, 4345275, 6783191, 10375943, 15578976, 22994469, 33408938, 47838207, 67580783, 94280764, 130001506, 177311376, 239383023

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/90720)*n^9 + (1/8064)*n^8 + (17/30240)*n^7 + (13/960)*n^6 - (131/4320)*n^5 + (181/384)*n^4 - (146161/90720)*n^3 + (171511/10080)*n^2 - (25129/504)*n + 58 for n>3.

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

G.f.: x*(4 - 22*x + 62*x^2 - 97*x^3 + 98*x^4 - 56*x^5 + 32*x^6 - 70*x^7 + 123*x^8 - 113*x^9 + 55*x^10 - 13*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..1....1..0..0....1..0..0....1..0..0....0..0..0....0..0..0
..1..1..0....1..1..1....0..0..1....0..0..1....0..0..0....0..1..1....0..1..1
..1..1..0....1..1..1....0..0..1....0..0..0....0..0..1....0..1..1....0..1..0
..1..0..0....1..1..0....0..0..0....0..0..0....0..0..1....0..1..0....0..0..1

Crossrefs

Column 3 of A227165.

Sequence in context: A192069 A073373 A292465 * A057414 A165910 A212766

Adjacent sequences: A227159 A227160 A227161 * A227163 A227164 A227165

Keyword

nonn

Author

R. H. Hardin, Jul 03 2013

Status

approved