A209594 Number of 3 X 3 0..n arrays with every element equal to a diagonal or antidiagonal reflection.

192, 3645, 28672, 140625, 513216, 1529437, 3932160, 9034497, 19000000, 37202781, 68677632, 120670225, 203297472, 330328125, 520093696, 796539777, 1190427840, 1740697597, 2496000000, 3516410961, 4875335872, 6661615005, 8981839872

Offset

1,1

Comments

Row 3 of A209593.

Links

R. H. Hardin, Table of n, a(n) for n = 1..50

Formula

a(n) = (n+1) ^ 6 * (2*n+1).

From Colin Barker, Jul 11 2018: (Start)

G.f.: x*(192 + 2109*x + 4888*x^2 + 2557*x^3 + 352*x^4 - 25*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.

(End)

Example

Some solutions for n=3:
..2..1..2....3..3..2....0..2..0....1..2..3....1..2..1....2..2..1....0..3..1
..1..3..2....3..1..1....2..2..0....2..3..1....0..2..2....2..3..0....2..1..3
..3..2..0....2..1..3....0..0..3....2..1..0....2..0..2....0..0..0....2..2..3

Prog

(PARI) a(n) = (2*n+1)*(n+1)^6; \\ Altug Alkan, Jul 11 2018

Crossrefs

Cf. A209593.

Sequence in context: A174384 A232919 A362738 * A168635 A299863 A223421

Adjacent sequences: A209591 A209592 A209593 * A209595 A209596 A209597

Keyword

nonn

Author

R. H. Hardin, Mar 10 2012

Status

approved