A190099 Number of 1:2:sqrt(5) proportioned triangles on an (n+1) X (n+1) grid.

0, 16, 64, 176, 384, 744, 1288, 2104, 3224, 4776, 6784, 9408, 12672, 16776, 21736, 27792, 34944, 43488, 53400, 65032, 78336, 93720, 111112, 130976, 153216, 178360, 206272, 237552, 272024, 310368, 352360, 398752, 449280, 504776, 564928, 630648

Offset

1,2

Comments

Diagonal of A190100.

Links

R. H. Hardin, Table of n, a(n) for n = 1..103

Formula

Empirical: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) +a(n-5) -3*a(n-6) +3*a(n-8) -a(n-9) +2*a(n-11) -2*a(n-12) -a(n-13) +a(n-14).

Empirical g.f.: 8*x^2*(2 + 2*x + 2*x^2 + 2*x^3 + x^4)*(1 + 2*x + 2*x^2 + 2*x^3 + 2*x^4) / ((1 - x)^5*(1 + x)^3*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 04 2018

Example

Some solutions for n=5:
  3 0   3 2   5 0   2 0   1 2   5 5   3 5   3 0   2 3   0 4
  1 0   2 1   3 0   1 1   1 0   1 5   2 4   2 1   0 3   1 5
  3 1   5 0   5 1   4 2   5 2   5 3   5 3   5 2   2 2   2 2

Crossrefs

Cf. A190100.

Sequence in context: A266103 A100184 A304845 * A316542 A306057 A059165

Adjacent sequences: A190096 A190097 A190098 * A190100 A190101 A190102

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved