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A202785 Number of 3 X 3 0..n arrays with row and column sums equal. 1
14, 87, 340, 1001, 2442, 5215, 10088, 18081, 30502, 48983, 75516, 112489, 162722, 229503, 316624, 428417, 569790, 746263, 964004, 1229865, 1551418, 1936991, 2395704, 2937505, 3573206, 4314519, 5174092, 6165545, 7303506, 8603647 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 3 of A202784.

LINKS

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

Robert Israel, Proof of empirical formula for A202785

Wikipedia, Ehrhart polynomial

FORMULA

Empirical: a(n) = (3/10)*n^5 + (3/2)*n^4 + (7/2)*n^3 + (9/2)*n^2 + (16/5)*n + 1.

Conjectures from Colin Barker, Jun 01 2018: (Start)

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

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Empirical formula verified (see link): Robert Israel, May 02 2019

EXAMPLE

Some solutions for n=7:

..3..2..1....3..5..5....0..6..2....0..7..5....4..2..1....5..6..0....1..6..1

..2..0..4....5..6..2....2..1..5....6..1..5....3..2..2....0..4..7....5..2..1

..1..4..1....5..2..6....6..1..1....6..4..2....0..3..4....6..1..4....2..0..6

MAPLE

seq((3/10)*n^5 + (3/2)*n^4 + (7/2)*n^3 + (9/2)*n^2 + (16/5)*n + 1, n=1..30); # Robert Israel, May 02 2019

CROSSREFS

Cf. A202784.

Sequence in context: A321941 A116343 A259473 * A255535 A034544 A248060

Adjacent sequences:  A202782 A202783 A202784 * A202786 A202787 A202788

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 24 2011

STATUS

approved

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Last modified January 18 19:32 EST 2020. Contains 331029 sequences. (Running on oeis4.)