A224145 Number of n X 7 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

29, 239, 1037, 3296, 8838, 21183, 46586, 95455, 184222, 337727, 592178, 998751, 1627894, 2574399, 3963306, 5956703, 8761486, 12638143, 17910626, 24977375, 34323558, 46534591, 62311002, 82484703, 108036734, 140116543, 180062866

Offset: 1

Author

R. H. Hardin, Mar 31 2013

Keywords

• nonn

Comments

Column 7 of A224146.

Examples

			Some solutions for n=3:
..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..0..0..0
..0..0..1..1..1..1..0....0..0..1..0..0..0..0....0..0..0..1..1..1..0
..0..0..1..1..1..1..1....0..0..1..0..0..0..0....0..0..0..1..1..1..1
		

Links

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

Crossrefs

Cf. A224146.

Formula

Empirical: a(n) = (4/315)*n^7 + (4/45)*n^6 + (34/45)*n^5 + (29/9)*n^4 + (508/45)*n^3 + (1156/45)*n^2 + (1328/35)*n - 161 for n>4.

Conjectures from Colin Barker, Aug 28 2018: (Start)

G.f.: x*(29 + 7*x - 63*x^2 + 68*x^3 + 152*x^4 - 199*x^5 + 28*x^6 + 71*x^7 - 21*x^8 - 12*x^9 + 3*x^10 + x^11) / (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>12.

(End)