OFFSET
1,2
COMMENTS
Column 2 of A199133.
a(n) is the last term in row n of triangle in A286030 (see also formulas below). Bob Selcoe, Sep 26 2021
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..198
FORMULA
Conjecture: a(3n+2) = a(3n+3) = A208881(n+1). - R. J. Mathar, Nov 01 2015
Conjecture: -(458*n-1205) *(n+2) *(n+1)*a(n) +(-208*n^3+2578*n^2-4613*n-2410) *a(n-1) +9*(-339*n-638) *a(n-2) +27*(n-2) *(458*n^2-289*n-1146) *a(n-3) +54*(n-2) *(n-3) *(104*n-1081) *a(n-4)=0. - R. J. Mathar, Nov 01 2015
Conjecture: (n+2)*(n+1)*a(n) +(5*n^2-2)*a(n-1) +3*(5*n^2-15*n+3) *a(n-2) +3*(n^2 -60*n +81)*a(n-3) +135*(-n^2+3*n-1)*a(n-4) -405*(n-2)*(n-4) *a(n-5) -810*(n-4) *(n-5) *a(n-6)=0. - R. J. Mathar, Nov 01 2015
From Bob Selcoe, Sep 26 2021: (Start)
When n == 0 (mod 3), a(n) = n!/(3*(n/3)!^3);
when n == 1 (mod 3), a(n) = n!/(((n+2)/3)!*((n-1)/3)!^2);
when n == 2 (mod 3), a(n) = n!/(((n-2)/3)!*((n+1)/3)!^2).
(End)
EXAMPLE
Some solutions for n=5:
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
1 0 1 2 1 2 1 2 1 0 1 2 1 0 1 2 1 2 1 0
0 2 2 0 0 1 2 0 0 2 2 1 0 2 0 1 2 0 2 1
2 1 0 2 2 0 0 1 2 1 1 0 2 0 1 2 0 1 1 2
0 2 2 1 0 2 2 0 1 2 0 2 1 2 2 0 1 2 2 0
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 03 2011
STATUS
approved