A190091 Number of rhombuses on a (n+1) X 3 grid.

2, 6, 10, 15, 20, 26, 32, 39, 46, 54, 62, 71, 80, 90, 100, 111, 122, 134, 146, 159, 172, 186, 200, 215, 230, 246, 262, 279, 296, 314, 332, 351, 370, 390, 410, 431, 452, 474, 496, 519, 542, 566, 590, 615, 640, 666, 692, 719, 746, 774, 802, 831, 860, 890, 920, 951, 982

Offset

1,1

Comments

Column 2 of A190098.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4).

Conjectures from Colin Barker, May 04 2018: (Start)

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

a(n) = (n^2 + 12*n - 4) / 4 for n even.

a(n) = (n^2 + 12*n - 5) / 4 for n odd.

(End)

Example

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

Crossrefs

Cf. A190098.

Sequence in context: A285959 A288631 A276211 * A343148 A331250 A186783

Adjacent sequences: A190088 A190089 A190090 * A190092 A190093 A190094

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved