A223963 Number of 3 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
64, 707, 3471, 12311, 36028, 92734, 217144, 471994, 965172, 1874532, 3482781, 6225291, 10754192, 18022648, 29393806, 46779538, 72814768, 111073890, 166336539, 244910775, 355022580, 507281450, 715232788, 996008770, 1371090364
Offset: 1
Keywords
Examples
Some solutions for n=3: ..0..0..1....2..2..2....0..0..2....0..0..2....0..2..3....0..1..3....1..2..2 ..1..1..1....1..2..2....0..2..3....1..1..1....0..1..3....1..2..3....0..1..3 ..0..1..3....1..1..3....3..3..3....1..1..2....0..0..2....1..1..3....0..0..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A223961.
Formula
Empirical: a(n) = (1/8640)*n^9 + (1/320)*n^8 + (503/10080)*n^7 + (659/1440)*n^6 + (3013/960)*n^5 + (37141/2880)*n^4 + (106019/2160)*n^3 - (18977/720)*n^2 + (2711/70)*n - 6 for n>2.
Conjectures from Colin Barker, Aug 24 2018: (Start)
G.f.: x*(64 + 67*x - 719*x^2 + 1736*x^3 - 2287*x^4 + 2271*x^5 - 2070*x^6 + 1632*x^7 - 910*x^8 + 311*x^9 - 58*x^10 + 5*x^11) / (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>12.
(End)
Comments