A190098 T(n,k)=Number of rhombuses on a (n+1)X(k+1) grid

1, 2, 2, 3, 6, 3, 4, 10, 10, 4, 5, 15, 22, 15, 5, 6, 20, 36, 36, 20, 6, 7, 26, 50, 66, 50, 26, 7, 8, 32, 66, 96, 96, 66, 32, 8, 9, 39, 82, 130, 151, 130, 82, 39, 9, 10, 46, 100, 164, 212, 212, 164, 100, 46, 10, 11, 54, 120, 204, 273, 312, 273, 204, 120, 54, 11, 12, 62, 142, 248, 344

Offset

1,2

Comments

Table starts

..1..2...3...4...5...6....7....8....9...10...11...12...13...14...15...16...17

..2..6..10..15..20..26...32...39...46...54...62...71...80...90..100..111..122

..3.10..22..36..50..66...82..100..120..142..164..188..212..238..264..292..320

..4.15..36..66..96.130..164..204..248..296..344..396..448..504..560..620..680

..5.20..50..96.151.212..273..344..421..504..587..676..765..860..959.1064.1169

..6.26..66.130.212.312..412..527..650..782..914.1059.1204.1358.1520.1691.1862

..7.32..82.164.273.412..564..736..918.1112.1306.1520.1734.1960.2198.2448.2698

..8.39.100.204.344.527..736..984.1244.1520.1796.2104.2412.2736.3076.3438.3800

..9.46.120.248.421.650..918.1244.1601.1978.2355.2776.3197.3638.4103.4600.5097

.10.54.142.296.504.782.1112.1520.1978.2478.2978.3535.4092.4674.5288.5945.6602

Links

R. H. Hardin, Table of n, a(n) for n = 1..5064

Formula

Empirical for column k: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>4,11,11,27,27,51,51,83,83,123,123,171,171 respectively for k=2..14

Example

Some solutions for n=5 k=3
..3..1....1..2....2..3....0..2....3..1....4..2....1..1....0..1....1..1....1..1
..4..0....1..3....3..1....1..0....3..2....4..3....1..3....2..0....2..3....2..0
..5..1....2..3....5..0....3..1....4..2....5..3....3..3....4..1....4..2....3..1
..4..2....2..2....4..2....2..3....4..1....5..2....3..1....2..2....3..0....2..2

Crossrefs

Diagonal is A189418(n+1)

Sequence in context: A051173 A322744 A128228 * A272973 A272958 A290632

Adjacent sequences: A190095 A190096 A190097 * A190099 A190100 A190101

Keyword

nonn,tabl

Author

R. H. Hardin May 04 2011

Status

approved