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

Author

R. H. Hardin May 04 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Diagonal is A189418(n+1)

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