A213801 Number of 3 X 3 0..n symmetric arrays with all rows summing to floor(n*3/2).

4, 13, 29, 57, 96, 153, 226, 323, 440, 587, 759, 967, 1204, 1483, 1796, 2157, 2556, 3009, 3505, 4061, 4664, 5333, 6054, 6847, 7696, 8623, 9611, 10683, 11820, 13047, 14344, 15737, 17204, 18773, 20421, 22177, 24016, 25969, 28010, 30171, 32424, 34803, 37279

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

a(n) = A064412(n+1) - A077043((2*n+1-(-1)^n)/4). - 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

Cf. A064412, A077403.

Sequence in context: A135039 A168559 A212247 * A301886 A015634 A266891

Adjacent sequences: A213798 A213799 A213800 * A213802 A213803 A213804

Keyword

nonn

Author

R. H. Hardin, Jun 20 2012

Status

approved