cp's OEIS Frontend

A223913 Number of n X 3 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A223913 #9 Aug 24 2018 03:59:11
%S A223913 22,158,666,2111,5548,12752,26494,50863,91634,156682,256442,404415,
%T A223913 617720,917692,1330526,1887967,2628046,3595862,4844410,6435455,
%U A223913 8440452,10941512,14032414,17819663,22423594,27979522,34638938,42570751,51962576
%N A223913 Number of n X 3 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A223913 Column 3 of A223918.
%H A223913 R. H. Hardin, <a href="/A223913/b223913.txt">Table of n, a(n) for n = 1..210</a>
%F A223913 Empirical: a(n) = (23/360)*n^6 + (23/40)*n^5 + (205/72)*n^4 + (143/24)*n^3 + (364/45)*n^2 + (82/15)*n - 1.
%F A223913 Conjectures from _Colin Barker_, Aug 24 2018: (Start)
%F A223913 G.f.: x*(22 + 4*x + 22*x^2 - 3*x^3 - 3*x^4 + 5*x^5 - x^6) / (1 - x)^7.
%F A223913 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A223913 (End)
%e A223913 Some solutions for n=3:
%e A223913 ..0..1..0....0..2..0....1..1..0....2..0..0....0..1..0....0..2..1....0..2..2
%e A223913 ..1..1..0....2..2..2....2..2..1....2..2..2....2..1..0....2..2..1....2..2..2
%e A223913 ..2..1..1....2..2..2....2..2..1....2..2..2....2..1..1....2..2..1....2..2..2
%Y A223913 Cf. A223918.
%K A223913 nonn
%O A223913 1,1
%A A223913 _R. H. Hardin_, Mar 29 2013