|
%I
%S 9,11,22,24,41,42,66,65,97,93,134,126,177,164,226,207,281,255,342,308,
%T 409,366,482,429,561,497,646,570,737,648,834,731,937,819,1046,912,
%U 1161,1010,1282,1113,1409,1221,1542,1334,1681,1452,1826,1575,1977,1703,2134
%N Number of (n+1) X (1+1) 0..2 arrays with row and column sums nondecreasing, and no adjacent elements equal.
%H R. H. Hardin, <a href="/A233402/b233402.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).
%F Conjectures from _Colin Barker_, Oct 11 2018: (Start)
%F G.f.: x*(9 + 11*x - 5*x^2 - 9*x^3 + 2*x^4 + 3*x^5) / ((1 - x)^3*(1 + x)^3).
%F a(n) = (62 - 14*(-1)^n + (50-6*(-1)^n)*n + (11+(-1)^(1+n))*n^2) / 16.
%F (End)
%e Some solutions for n=5:
%e ..2..0....0..1....0..1....1..0....0..1....0..2....0..1....1..0....1..0....0..1
%e ..0..2....1..0....1..0....0..2....1..0....2..0....1..0....0..1....0..1....1..0
%e ..2..0....0..2....0..2....2..0....0..1....0..2....0..2....1..0....2..0....2..1
%e ..0..2....2..0....2..0....1..2....1..0....2..1....2..1....0..2....0..2....1..2
%e ..2..1....0..2....0..2....2..1....2..1....1..2....1..2....2..1....2..1....2..1
%e ..1..2....2..1....2..0....1..2....1..2....2..1....2..1....1..2....1..2....1..2
%Y Column 1 of A233408.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 09 2013
|
