A202919 Number of n X 3 nonnegative integer arrays with each row and column increasing from zero by 0, 1, 2 or 3.

1, 10, 90, 534, 2310, 8012, 23661, 61830, 146718, 321970, 662233, 1289652, 2396745, 4277352, 7367630, 12299364, 19968183, 31619610, 48956236, 74269690, 110601480, 161937204, 233439075, 331722170, 465180300, 644367906, 882444915, 1195692040

Offset

1,2

Comments

Column 3 of A202924.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/17280)*n^9 + (23/20160)*n^8 + (193/20160)*n^7 + (13/288)*n^6 + (523/5760)*n^5 + (1/2880)*n^4 + (29/4320)*n^3 + (457/1008)*n^2 + (11/28)*n.

Conjectures from Colin Barker, Jun 02 2018: (Start)

G.f.: x*(1 + 35*x^2 - 36*x^3 + 30*x^4 - 10*x^5 + x^6) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

Example

Some solutions for n=5:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..2..2....0..1..1....0..0..1....0..0..2....0..0..2....0..0..2....0..0..1
..0..2..3....0..1..1....0..2..2....0..1..4....0..1..2....0..1..2....0..0..2
..0..3..6....0..3..3....0..3..5....0..3..5....0..1..2....0..1..2....0..0..2
..0..3..6....0..3..4....0..3..6....0..3..5....0..2..2....0..2..5....0..2..5

Crossrefs

Cf. A202924.

Sequence in context: A192898 A044261 A065690 * A202576 A201723 A228418

Adjacent sequences: A202916 A202917 A202918 * A202920 A202921 A202922

Keyword

nonn

Author

R. H. Hardin, Dec 26 2011

Status

approved