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

Author

R. H. Hardin Apr 28 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is -A147973(n+4)

Diagonal is A077435(n+1)

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