|
%I #9 May 25 2018 11:14:01
%S 4,30,72,131,208,304,420,557,716,898,1104,1335,1592,1876,2188,2529,
%T 2900,3302,3736,4203,4704,5240,5812,6421,7068,7754,8480,9247,10056,
%U 10908,11804,12745,13732,14766,15848,16979,18160,19392,20676,22013,23404,24850
%N Number of n X 2 0..3 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.
%C Column 2 of A201981.
%H R. H. Hardin, <a href="/A201975/b201975.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/6)*n^3 + 7*n^2 + (23/6)*n - 7.
%F Conjectures from _Colin Barker_, May 25 2018: (Start)
%F G.f.: x*(4 + 14*x - 24*x^2 + 7*x^3) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F (End)
%e Some solutions for n=9.
%e ..0..3....1..3....0..3....0..3....1..3....0..3....0..3....1..2....0..3....0..1
%e ..0..3....1..3....0..3....0..3....2..2....0..3....1..2....3..1....0..3....3..0
%e ..1..2....1..3....0..3....0..3....2..2....0..3....1..2....3..1....1..2....3..0
%e ..1..2....1..3....0..3....0..3....2..2....0..3....1..2....3..1....2..1....3..0
%e ..1..2....1..3....2..0....0..3....2..2....2..1....1..2....3..1....2..1....3..0
%e ..2..0....1..3....2..0....1..2....2..2....2..1....1..2....3..1....2..1....3..0
%e ..2..0....2..2....2..0....1..2....2..2....2..1....1..2....3..1....3..0....3..0
%e ..2..0....3..1....2..0....1..2....3..0....2..1....3..1....3..1....3..0....3..0
%e ..2..0....3..1....2..0....2..1....3..0....2..1....3..1....3..1....3..0....3..0
%Y Cf. A201981.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 07 2011
| 