A223927 - OEIS

%I #7 Feb 21 2018 09:22:34

%S 9,54,218,698,1915,4690,10511,21919,43045,80334,143496,246728,410255,

%T 662242,1041133,1598477,2402305,3541126,5128614,7309062,10263683,

%U 14217842,19449307,26297611,35174621,46576414,61096564,79440948

%N Number of n X 2 0..2 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.

%C Column 2 of A223933.

%H R. H. Hardin, <a href="/A223927/b223927.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/10080)*n^8 + (1/504)*n^7 + (1/40)*n^6 + (109/720)*n^5 + (379/480)*n^4 + (317/144)*n^3 + (8027/2520)*n^2 + (691/420)*n + 1.

%F Conjectures from _Colin Barker_, Feb 21 2018: (Start)

%F G.f.: x*(9 - 27*x + 56*x^2 - 76*x^3 + 79*x^4 - 59*x^5 + 29*x^6 - 8*x^7 + x^8) / (1 - x)^9.

%F 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.

%F (End)

%e Some solutions for n=3:

%e ..2..1....0..0....1..1....1..0....0..0....0..0....1..2....0..0....2..1....0..2

%e ..2..2....1..0....1..2....0..2....1..2....0..2....2..2....0..2....0..2....0..2

%e ..1..2....2..2....2..1....0..1....0..1....1..0....2..2....0..0....0..0....0..0

%Y Cf. A223933.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 29 2013