OFFSET
0,5
COMMENTS
Count of triangular numbers between powers of 2.
a(n)/a(n-1) converges to sqrt(2) (A002193). [John W. Nicholson, May 16 2011]
Essentially first differences of A017911. - Jeremy Gardiner, Aug 11 2013. Also second differences of A001521. - N. J. A. Sloane, Apr 27 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
EXAMPLE
Between 2^(6-1)=32 and 2^6=64 are T(8)=36, T(9)=45, T(10)=55 so A190660(6)=3.
MATHEMATICA
TriangularIndex[n_] := (-1 + Sqrt[1 + 8*n])/2; Differences[Table[Floor[TriangularIndex[2^n]], {n, -1, 50}]] (* T. D. Noe, May 19 2011 *)
PROG
(PARI) a(n) = if (n==0, 1, sum(i=2^(n-1)+1, 2^n, ispolygonal(i, 3))); \\ Michel Marcus, Apr 28 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Nicholson, May 16 2011
EXTENSIONS
Extended by T. D. Noe, May 19 2011
STATUS
approved