A201445 - OEIS

%I #8 May 23 2018 06:37:00

%S 6,2,21,9,56,13,110,32,198,41,315,78,480,94,684,155,950,180,1265,271,

%T 1656,307,2106,434,2646,483,3255,652,3968,716,4760,933,5670,1014,6669,

%U 1285,7800,1385,9030,1716,10406,1837,11891,2234,13536,2378,15300,2847

%N Number of n X 2 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

%C Column 2 of A201451.

%H R. H. Hardin, <a href="/A201445/b201445.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-2) +3*a(n-4) -3*a(n-6) -3*a(n-8) +3*a(n-10) +a(n-12) -a(n-14).

%F Subsequences for n modulo 4 = 1,2,3,0:

%F p=(n+3)/4: a(n) = 8*p^3 - 2*p^2

%F q=(n+2)/4: a(n) = (4/3)*q^3 + (1/2)*q^2 + (1/6)*q

%F r=(n+1)/4: a(n) = 8*r^3 + 10*r^2 + 3*r

%F s=(n+0)/4: a(n) = (4/3)*s^3 + (7/2)*s^2 + (19/6)*s + 1.

%F Empirical g.f.: x*(6 + 2*x + 15*x^2 + 7*x^3 + 17*x^4 - 2*x^5 + 9*x^6 - 2*x^7 + x^8 + 3*x^9 + x^11 - x^13) / ((1 - x)^4*(1 + x)^4*(1 + x^2)^3). - _Colin Barker_, May 23 2018

%e Some solutions for n=10:

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

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

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

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

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

%e ..1..2....1..2....1..2....1..3....1..3....2..2....1..3....2..2....1..2....1..2

%e ..1..2....1..2....1..2....1..3....1..3....2..3....1..3....2..3....1..3....1..3

%e ..1..3....2..3....1..3....1..3....1..3....2..3....1..3....2..3....2..3....1..3

%e ..3..3....3..3....3..3....2..3....1..3....2..3....2..3....2..3....2..3....2..3

%e ..3..3....3..3....3..3....2..3....1..3....3..3....2..3....3..3....3..3....3..3

%Y Cf. A201451.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 01 2011