A189895 T(n,k) = Number of isosceles right triangles on a (n+1) X (k+1) grid.

4, 10, 10, 16, 28, 16, 22, 50, 50, 22, 28, 74, 96, 74, 28, 34, 98, 150, 150, 98, 34, 40, 122, 208, 244, 208, 122, 40, 46, 146, 268, 350, 350, 268, 146, 46, 52, 170, 328, 464, 516, 464, 328, 170, 52, 58, 194, 388, 582, 700, 700, 582, 388, 194, 58, 64, 218, 448, 702, 896, 968

Offset

1,1

Comments

Table starts

..4..10..16..22...28...34...40...46...52...58...64...70...76....82....88....94

.10..28..50..74...98..122..146..170..194..218..242..266..290...314...338...362

.16..50..96.150..208..268..328..388..448..508..568..628..688...748...808...868

.22..74.150.244..350..464..582..702..822..942.1062.1182.1302..1422..1542..1662

.28..98.208.350..516..700..896.1100.1308.1518.1728.1938.2148..2358..2568..2778

.34.122.268.464..700..968.1260.1570.1892.2222.2556.2892.3228..3564..3900..4236

.40.146.328.582..896.1260.1664.2100.2560.3038.3528.4026.4528..5032..5536..6040

.46.170.388.702.1100.1570.2100.2680.3300.3952.4628.5322.6028..6742..7460..8180

.52.194.448.822.1308.1892.2560.3300.4100.4950.5840.6762.7708..8672..9648.10632

.58.218.508.942.1518.2222.3038.3952.4950.6020.7150.8330.9550.10802.12078.13372

Links

R. H. Hardin, Table of n, a(n) for n = 1..10025

Formula

Empirical for column k: a(n) = k*(k+1)*(k+2)*n + b(k) for n>2*k-2.

k=1: a(n) = 6*n - 2

k=2: a(n) = 24*n - 22 for n>2

k=3: a(n) = 60*n - 92 for n>4

k=4: a(n) = 120*n - 258 for n>6

k=5: a(n) = 210*n - 582 for n>8

k=6: a(n) = 336*n - 1140 for n>10

k=7: a(n) = 504*n - 2024 for n>12

k=8: a(n) = 720*n - 3340 for n>14

k=9: a(n) = 990*n - 5210 for n>16

k=10: a(n) = 1320*n - 7770 for n>18

k=11: a(n) = 1716*n - 11172 for n>20

k=12: a(n) = 2184*n - 15582 for n>22

k=13: a(n) = 2730*n - 21182 for n>24

k=14: a(n) = 3360*n - 28168 for n>26

Example

Some solutions for n=7 k=5
..3..5....1..1....5..4....6..4....5..1....4..4....3..2....2..5....4..3....2..3
..1..4....2..4....1..3....3..5....4..3....1..1....4..1....0..1....2..3....0..0
..4..3....4..0....6..0....5..1....7..2....7..1....4..3....6..3....4..1....5..1

Crossrefs

Diagonal is A187452(n+1).

(2n-1,n) diagonal is A189894.

Sequence in context: A264272 A264257 A111072 * A310333 A180862 A310334

Adjacent sequences: A189892 A189893 A189894 * A189896 A189897 A189898

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 30 2011

Status

approved