A190092 Number of rhombuses on a (n+1) X 4 grid.

3, 10, 22, 36, 50, 66, 82, 100, 120, 142, 164, 188, 212, 238, 264, 292, 320, 350, 380, 412, 444, 478, 512, 548, 584, 622, 660, 700, 740, 782, 824, 868, 912, 958, 1004, 1052, 1100, 1150, 1200, 1252, 1304, 1358, 1412, 1468, 1524, 1582, 1640, 1700, 1760, 1822, 1884

Offset

1,1

Comments

Column 3 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) for n>11.

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

G.f.: x*(3 + 4*x + 2*x^2 - 2*x^3 - 5*x^4 + 2*x^8 - 2*x^10) / ((1 - x)^3*(1 + x)).

a(n) = (n^2 + 24*n - 56) / 2 for n>7 and even.

a(n) = (n^2 + 24*n - 57) / 2 for n>7 and odd.

(End)

Example

Some solutions for n=4:
..0..0....0..2....3..1....1..2....0..0....1..1....3..0....1..0....1..3....0..1
..1..2....2..1....3..2....2..1....0..1....2..3....3..1....1..2....2..1....1..3
..3..3....4..2....4..2....3..2....1..1....4..2....4..1....3..2....4..0....3..2
..2..1....2..3....4..1....2..3....1..0....3..0....4..0....3..0....3..2....2..0

Crossrefs

Cf. A190098.

Sequence in context: A068082 A058077 A161672 * A174459 A326124 A346166

Adjacent sequences: A190089 A190090 A190091 * A190093 A190094 A190095

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved