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 A189895 T(n,k) = Number of isosceles right triangles on a (n+1) X (k+1) grid. 2

%I

%S 4,10,10,16,28,16,22,50,50,22,28,74,96,74,28,34,98,150,150,98,34,40,

%T 122,208,244,208,122,40,46,146,268,350,350,268,146,46,52,170,328,464,

%U 516,464,328,170,52,58,194,388,582,700,700,582,388,194,58,64,218,448,702,896,968

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

%C Table starts

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

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

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

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

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

%C .34.122.268.464..700..968.1260.1570.1892.2222.2556.2892.3228..3564..3900..4236

%C .40.146.328.582..896.1260.1664.2100.2560.3038.3528.4026.4528..5032..5536..6040

%C .46.170.388.702.1100.1570.2100.2680.3300.3952.4628.5322.6028..6742..7460..8180

%C .52.194.448.822.1308.1892.2560.3300.4100.4950.5840.6762.7708..8672..9648.10632

%C .58.218.508.942.1518.2222.3038.3952.4950.6020.7150.8330.9550.10802.12078.13372

%H R. H. Hardin, <a href="/A189895/b189895.txt">Table of n, a(n) for n = 1..10025</a>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

%e Some solutions for n=7 k=5

%e ..3..5....1..1....5..4....6..4....5..1....4..4....3..2....2..5....4..3....2..3

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

%e ..4..3....4..0....6..0....5..1....7..2....7..1....4..3....6..3....4..1....5..1

%Y Diagonal is A187452(n+1).

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Apr 30 2011

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Last modified May 29 07:49 EDT 2022. Contains 354122 sequences. (Running on oeis4.)