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
Examples
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
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
Comments