A189894 Number of isosceles right triangles on a 2n X (n+1) grid.

4, 50, 208, 582, 1308, 2556, 4528, 7460, 11620, 17310, 24864, 34650, 47068, 62552, 81568, 104616, 132228, 164970, 203440, 248270, 300124, 359700, 427728, 504972, 592228, 690326, 800128, 922530, 1058460, 1208880, 1374784, 1557200, 1757188

Offset

1,1

Comments

(2n-1,n) diagonal through A189895.

Links

R. H. Hardin, Table of n, a(n) for n = 1..71

Formula

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6).

Empirical: a(n) = -1/16 +11*n^4/8 +7*n^3/2 +3*n^2/4 -3*n/2 +(-1)^n/16 with g.f. -2*x*(2+17*x+14*x^2)/ ((1+x)*(x-1)^5). - R. J. Mathar, May 18 2011

Example

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

Crossrefs

Cf. A189895.

Sequence in context: A254543 A321590 A274872 * A275291 A240396 A197473

Adjacent sequences: A189891 A189892 A189893 * A189895 A189896 A189897

Keyword

nonn

Author

R. H. Hardin Apr 30 2011

Status

approved