

A190660


Number of triangular numbers T(k) between powers of 2, 2^(n1) < T(k) <= 2^n.


3



1, 0, 1, 1, 2, 2, 3, 5, 7, 9, 13, 19, 27, 37, 53, 75, 106, 150, 212, 300, 424, 600, 848, 1200, 1697, 2399, 3393, 4799, 6786, 9598, 13573, 19195, 27146, 38390, 54292, 76780, 108584, 153560, 217167, 307121, 434334, 614242, 868669, 1228483, 1737338, 2456966
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OFFSET

0,5


COMMENTS

Count of triangular numbers between powers of 2.
a(n)/a(n1) 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^(61)=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^(n1)+1, 2^n, ispolygonal(i, 3))); \\ Michel Marcus, Apr 28 2014


CROSSREFS

Cf. A001521, A002193, A017911.
Sequence in context: A125505 A061565 A077075 * A180158 A320689 A173693
Adjacent sequences: A190657 A190658 A190659 * A190661 A190662 A190663


KEYWORD

nonn


AUTHOR

John W. Nicholson, May 16 2011


EXTENSIONS

Extended by T. D. Noe, May 19 2011


STATUS

approved



