A223766 Number of n X 4 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.
11, 56, 155, 361, 782, 1601, 3141, 5907, 10678, 18618, 31422, 51505, 82243, 128276, 195884, 293448, 432009, 625939, 893739, 1258980, 1751404, 2408203, 3275495, 4410017, 5881056, 7772640, 10186012, 13242411, 17086185, 21888262, 27850006
Offset: 1
Keywords
Examples
Some solutions for n=3: ..1..1..1..0....0..0..1..1....0..0..1..0....1..0..0..0....0..1..1..0 ..0..1..1..1....0..1..1..1....1..1..1..1....0..1..0..0....0..1..1..1 ..0..1..1..1....1..1..1..1....1..1..1..1....0..0..1..1....0..0..1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A223770.
Formula
Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 + (3/320)*n^6 + (1/45)*n^5 + (1109/1920)*n^4 - (4837/1440)*n^3 + (422483/10080)*n^2 - (109337/840)*n + 226 for n>4.
Conjectures from Colin Barker, Aug 22 2018: (Start)
G.f.: x*(11 - 43*x + 47*x^2 + 58*x^3 - 205*x^4 + 209*x^5 - 42*x^6 - 150*x^7 + 256*x^8 - 245*x^9 + 151*x^10 - 55*x^11 + 9*x^12) / (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>13.
(End)
Comments