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A202919 Number of n X 3 nonnegative integer arrays with each row and column increasing from zero by 0, 1, 2 or 3. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 06:18 EDT 2021. Contains 347596 sequences. (Running on oeis4.)