OFFSET
1,1
COMMENTS
Row 3 of A213800.
Sequence is difference between numbers of triangles, regardless of size, in A064412 (a family of ((3*n^2+3*n+2)/2)-iamonds, see also illustration of initial terms there) and a quantity A077043 of triangles of dimension 1. - Luce ETIENNE, Aug 23 2014
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 2*a(n-1) -2*a(n-3) +2*a(n-4) -2*a(n-5) +2*a(n-7) -a(n-8).
Empirical: G.f. -x*(-4-5*x-3*x^2-7*x^3-x^5-2*x^6+x^7) / ( (x^2+1)*(1+x)^2*(x-1)^4 ). - R. J. Mathar, Jul 04 2012
a(n) = (14*n^3+42*n^2+53*n+25+3*(n+1)*(-1)^n+2*((-1)^((2*n+1-(-1)^n)/4)-(-1)^((6*n+5-(-1)^n)/4)))/32. - Luce ETIENNE, Aug 23 2014
EXAMPLE
Some solutions for n=4:
..1..3..2....2..4..0....0..4..2....1..2..3....1..1..4....4..0..2....2..2..2
..3..1..2....4..0..2....4..0..2....2..2..2....1..3..2....0..2..4....2..2..2
..2..2..2....0..2..4....2..2..2....3..2..1....4..2..0....2..4..0....2..2..2
a(2)=5-1=4, a(3)=14-1=13, a(210)=4118206-8269=4109937. - Luce ETIENNE, Aug 23 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jun 20 2012
STATUS
approved