A190093 Number of rhombuses on an (n+1) X 5 grid.

4, 15, 36, 66, 96, 130, 164, 204, 248, 296, 344, 396, 448, 504, 560, 620, 680, 744, 808, 876, 944, 1016, 1088, 1164, 1240, 1320, 1400, 1484, 1568, 1656, 1744, 1836, 1928, 2024, 2120, 2220, 2320, 2424, 2528, 2636, 2744, 2856, 2968, 3084, 3200, 3320, 3440

Offset

1,1

Comments

Column 4 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*(4 + 7*x + 6*x^2 + 2*x^3 - 10*x^4 - 5*x^5 + 2*x^7 + 4*x^8 - 2*x^9 - 4*x^10) / ((1 - x)^3*(1 + x)).

a(n) = n^2 + 28*n - 84 for n>7 and even.

a(n) = n^2 + 28*n - 85 for n>7 and odd.

(End)

Example

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

Crossrefs

Cf. A190098.

Sequence in context: A209345 A323452 A330204 * A077414 A304487 A350689

Adjacent sequences: A190090 A190091 A190092 * A190094 A190095 A190096

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved