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A202786 Number of 4 X 4 0..n arrays with row and column sums equal 2
140, 5673, 89520, 790425, 4756140, 21841937, 82112704, 264639729, 754898668, 1950230969, 4641494832, 10309971465, 21592075596, 42980713761, 81851507456, 149924818657, 265300850124, 455235310153, 759857498672, 1237071456633 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 4 of A202784

From Robert Israel, May 03 2019: (Start)

a(n) is the number of integer lattice points in n*C where C is the polytope in R^(4 X 4) defined by Sum_{1<=i<=4} x_{i,j} = Sum_{1<=i<=4} x_{j,i} = Sum_{1<=i<=4} x_{i,1} for 1<=j<=4 and 0 <= x_{i,j} <= 1 for 1<=i,j<=4.

The vertices of this polytope have coordinates in {0,1/2,1} (an example of a vertex with non-integer coordinates is [0,1,1,1/2; 1,0,1,1/2; 1,1,0,1/2; 1/2,1/2,1/2,1]).

Therefore a(n) should be quasi-polynomial in n. (End)

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..21

Wikipedia, Ehrhart quasi-polynomials

FORMULA

Conjecture: a(n) = (29 + 3*(-1)^n)/32 + (34/7)*n + (7202/525)*n^2 + (4658/189)*n^3 + (118873/3780)*n^4 + (5321/180)*n^5 + (36827/1800)*n^6 + (1285/126)*n^7 + (17581/5040)*n^8 + (2789/3780)*n^9 + (2789/37800)*n^10. - Robert Israel, May 03 2019

EXAMPLE

Some solutions for n=3

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

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

..3..1..3..1....2..1..1..2....1..1..1..3....2..1..2..3....3..2..1..1

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

CROSSREFS

Sequence in context: A061607 A223349 A282613 * A035820 A075915 A159362

Adjacent sequences:  A202783 A202784 A202785 * A202787 A202788 A202789

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 24 2011

STATUS

approved

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Last modified May 26 21:56 EDT 2022. Contains 354092 sequences. (Running on oeis4.)