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

1,1

Comments

Column 7 of A224146.

Links

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

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)

Example

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

Crossrefs

Cf. A224146.

Sequence in context: A223837 A126426 A126425 * A225009 A177419 A142559

Adjacent sequences: A224142 A224143 A224144 * A224146 A224147 A224148

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved