A223633 Number of n X 4 0..1 arrays with rows, antidiagonals and columns unimodal.
11, 121, 801, 3712, 13599, 42109, 114713, 282273, 639165, 1350228, 2689169, 5091414, 9224755, 16081503, 27096217, 44293439, 70470225, 109418622, 166193601, 247432316, 361730919, 520085521, 736404249, 1028097709, 1416755525
Offset: 1
Keywords
Examples
Some solutions for n=4: ..0..0..1..0....0..1..1..0....1..0..0..0....0..0..0..1....0..1..0..0 ..0..1..1..1....0..1..1..0....1..0..0..0....0..1..1..0....0..1..1..0 ..1..1..1..1....0..1..1..0....1..1..0..0....1..1..1..0....0..0..0..1 ..1..0..0..0....1..1..1..1....0..1..1..0....0..1..0..0....0..0..0..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A223637.
Formula
Empirical: a(n) = (1/112)*n^8 - (1/72)*n^7 + (203/360)*n^6 + (37/360)*n^5 + (41/144)*n^4 + (901/36)*n^3 - (168481/2520)*n^2 + (5693/60)*n - 45 for n>2.
Conjectures from Colin Barker, Aug 21 2018: (Start)
G.f.: x*(11 + 22*x + 108*x^2 - 65*x^3 + 249*x^4 - 74*x^5 + 92*x^6 + 18*x^7 + 9*x^8 - 11*x^9 + x^10) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>11.
(End)
Comments