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

Author

R. H. Hardin, Jul 03 2013

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Column 3 of A227165.

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)