A224147 Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
4, 16, 49, 124, 275, 554, 1037, 1831, 3082, 4984, 7789, 11818, 17473, 25250, 35753, 49709, 67984, 91600, 121753, 159832, 207439, 266410, 338837, 427091, 533846, 662104, 815221, 996934, 1211389, 1463170, 1757329, 2099417, 2495516, 2952272
Offset: 1
Keywords
Examples
Some solutions for n=3: ..0..0..0....0..0..0....0..0..1....0..1..0....0..0..0....0..0..0....0..0..0 ..0..1..1....0..0..0....0..0..1....0..1..0....0..0..1....1..0..0....1..1..1 ..1..1..1....0..0..0....0..1..1....0..1..0....0..0..1....1..1..0....1..1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A224146.
Formula
Empirical: a(n) = (1/720)*n^6 + (1/80)*n^5 + (23/144)*n^4 + (29/48)*n^3 + (241/180)*n^2 + (53/60)*n + 1.
Conjectures from Colin Barker, Aug 28 2018: (Start)
G.f.: x*(4 - 12*x + 21*x^2 - 23*x^3 + 16*x^4 - 6*x^5 + x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
Comments