A189814 T(n,k)=Number of right triangles on a (n+1)X(k+1) grid

4, 14, 14, 28, 44, 28, 46, 94, 94, 46, 68, 158, 200, 158, 68, 94, 238, 342, 342, 238, 94, 124, 330, 524, 596, 524, 330, 124, 158, 434, 732, 926, 926, 732, 434, 158, 196, 550, 972, 1308, 1444, 1308, 972, 550, 196, 238, 678, 1236, 1754, 2060, 2060, 1754, 1236, 678

Offset

1,1

Comments

Table starts

...4..14...28...46...68...94...124...158...196...238...284...334...388...446

..14..44...94..158..238..330...434...550...678...818...970..1134..1310..1498

..28..94..200..342..524..732...972..1236..1524..1840..2180..2544..2932..3344

..46.158..342..596..926.1308..1754..2250..2794..3390..4026..4702..5426..6190

..68.238..524..926.1444.2060..2784..3596..4492..5470..6516..7630..8820.10070

..94.330..732.1308.2060.2960..4032..5250..6604..8082..9684.11388.13220.15144

.124.434..972.1754.2784.4032..5520..7224..9128.11218.13500.15938.18568.21328

.158.550.1236.2250.3596.5250..7224..9496.12044.14860.17948.21266.24852.28634

.196.678.1524.2794.4492.6604..9128.12044.15332.18990.23012.27354.32052.37032

.238.818.1840.3390.5470.8082.11218.14860.18990.23596.28678.34190.40166.46522

Links

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

Formula

Empirical for columns

k=1: a(n) = 2*n^2 + 4*n - 2

k=2: a(n) = 6*n^2 + 26*n - 42 for n>3

k=3: a(n) = 12*n^2 + 88*n - 240 for n>8

k=4: a(n) = 20*n^2 + 228*n - 930 for n>15

k=5: a(n) = 30*n^2 + 468*n - 2478 for n>24

k=6: a(n) = 42*n^2 + 886*n - 6080 for n>35

k=7: a(n) = 56*n^2 + 1480*n - 12216 for n>48

k=8: a(n) = 72*n^2 + 2344*n - 23112 for n>63

k=9: a(n) = 90*n^2 + 3516*n - 40434 for n>80

k=10: a(n) = 110*n^2 + 5090*n - 67626 for n>99

k=11: a(n) = 132*n^2 + 7016*n - 105016 for n>120

k=12: a(n) = 156*n^2 + 9564*n - 162094 for n>143

k=13: a(n) = 182*n^2 + 12572*n - 236518 for n>168

k=14: a(n) = 210*n^2 + 16230*n - 337676 for n>195

Example

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

Crossrefs

Column 1 is -A147973(n+4)

Diagonal is A077435(n+1)

Sequence in context: A276703 A170847 A168420 * A200553 A229392 A229320

Adjacent sequences: A189811 A189812 A189813 * A189815 A189816 A189817

Keyword

nonn,tabl

Author

R. H. Hardin Apr 28 2011

Status

approved