A223719 Number of n X 2 0..2 arrays with rows, antidiagonals and columns unimodal.
9, 81, 484, 2116, 7396, 21904, 57121, 134689, 292681, 594441, 1140624, 2085136, 3655744, 6180196, 10118761, 16104169, 24990001, 37908649, 56340036, 82192356, 117896164, 166513216, 231861529, 318658201, 432681601, 580954609, 771950656
Offset: 1
Keywords
Examples
Some solutions for n=3: ..1..0....2..0....1..2....2..0....1..1....2..0....0..2....2..1....1..1....2..2 ..1..2....1..2....1..2....0..0....2..2....2..1....2..0....1..1....2..1....1..2 ..2..1....1..0....1..2....0..1....0..1....0..0....2..0....1..2....1..1....1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = (1/576)*n^8 + (1/48)*n^7 + (41/288)*n^6 + (13/24)*n^5 + (793/576)*n^4 + (31/16)*n^3 + (119/48)*n^2 + (3/2)*n + 1.
Conjectures from Colin Barker, Feb 19 2018: (Start)
G.f.: x*(9 + 79*x^2 - 80*x^3 + 106*x^4 - 68*x^5 + 31*x^6 - 8*x^7 + x^8) / (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>9.
(End)
Comments