A249753 Number of triangles in the complex obtained by starting with an isosceles right triangle, and dividing each cell into two similar isosceles right triangles n times.

1, 3, 7, 17, 40, 99, 246, 642, 1690, 4554, 12436, 34132, 95230, 263934, 744956, 2075132, 5892430, 16456014, 46871196, 131068572, 373897870, 1046231694, 2986898716, 8360588572, 23878057870, 66847653774, 190955945756, 534633021212, 1527373517710, 4276471354254

Offset: 0

Author

Robin Houston, Nov 04 2014

Keywords

• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• "Marsland", Reddit discussion

Formula

a(0) = 1;

a(1) = 3;

a(2) = 7;

a(2k+1) = (140 2^(3k) + 318 2^(2k) + 60 2^(k) - 48 + 16 (-1)^(k)) / 144, for k > 0;

a(2k) = (50 2^(3k) + 147 2^(2k) + 60 2^(k) - 48 + 16 (-1)^(k)) / 144, for k > 1.

Empirical g.f.: -(16*x^11 +8*x^10 +14*x^9 -7*x^8 -33*x^7 -8*x^6 -13*x^5 -13*x^4 +16*x^3 +9*x^2 -2*x -1) / ((x -1)*(2*x -1)*(2*x +1)*(x^2 +1)*(2*x^2 -1)*(8*x^2 -1)). - Colin Barker, Nov 14 2014