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A202807 Number of n X 3 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2. 1
1, 6, 32, 121, 356, 881, 1925, 3830, 7083, 12352, 20526, 32759, 50518, 75635, 110363, 157436, 220133, 302346, 408652, 544389, 715736, 929797, 1194689, 1519634, 1915055, 2392676, 2965626, 3648547, 4457706, 5411111, 6528631, 7832120, 9345545 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 3 of A202812.

LINKS

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

FORMULA

Empirical: a(n) = (1/180)*n^6 + (1/20)*n^5 + (13/72)*n^4 - (67/360)*n^2 + (19/20)*n.

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

G.f.: x*(1 - x + 11*x^2 - 12*x^3 + 6*x^4 - x^5) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(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 0 0    0 0 1    0 0 1    0 0 0    0 1 2    0 1 1    0 0 0

  0 1 2    0 0 1    0 0 1    0 0 0    0 1 2    0 1 1    0 0 2

  0 2 2    0 2 3    0 1 3    0 0 2    0 2 2    0 2 2    0 1 2

  0 2 4    0 2 3    0 2 4    0 1 3    0 2 2    0 2 2    0 2 2

CROSSREFS

Cf. A202812.

Sequence in context: A200765 A239573 A130410 * A203324 A027217 A245128

Adjacent sequences:  A202804 A202805 A202806 * A202808 A202809 A202810

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 24 2011

STATUS

approved

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Last modified September 15 08:37 EDT 2019. Contains 327062 sequences. (Running on oeis4.)