A190098 - OEIS

%I #5 Mar 31 2012 12:36:19

%S 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,

%T 7,8,32,66,96,96,66,32,8,9,39,82,130,151,130,82,39,9,10,46,100,164,

%U 212,212,164,100,46,10,11,54,120,204,273,312,273,204,120,54,11,12,62,142,248,344

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

%C Table starts

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

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

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

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

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

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

%C ..7.32..82.164.273.412..564..736..918.1112.1306.1520.1734.1960.2198.2448.2698

%C ..8.39.100.204.344.527..736..984.1244.1520.1796.2104.2412.2736.3076.3438.3800

%C ..9.46.120.248.421.650..918.1244.1601.1978.2355.2776.3197.3638.4103.4600.5097

%C .10.54.142.296.504.782.1112.1520.1978.2478.2978.3535.4092.4674.5288.5945.6602

%H R. H. Hardin, <a href="/A190098/b190098.txt">Table of n, a(n) for n = 1..5064</a>

%F 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

%e Some solutions for n=5 k=3

%e ..3..1....1..2....2..3....0..2....3..1....4..2....1..1....0..1....1..1....1..1

%e ..4..0....1..3....3..1....1..0....3..2....4..3....1..3....2..0....2..3....2..0

%e ..5..1....2..3....5..0....3..1....4..2....5..3....3..3....4..1....4..2....3..1

%e ..4..2....2..2....4..2....2..3....4..1....5..2....3..1....2..2....3..0....2..2

%Y Diagonal is A189418(n+1)

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ May 04 2011