OFFSET
0,3
COMMENTS
Original definition: The binary representation of each integer in the sequence consists of a single leading bit, followed by a string of n-1 zeros, followed by the previous integer. i.e. 3 = 2^1 + 1, 11 = 2^(2+1) + 3, 75 = 2^(3+2+1) + 11, and so on.
Numbers in this sequence may be used as a multiplier in hash functions to scatter and interleave bits.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..82
FORMULA
a(n) = Sum_{k=1..n} A006125(k). - R. J. Mathar, Oct 18 2010
a(n) = a(n-1) + 2*(a(n-1) - a(n-2))^2/(a(n-2) - a(n-3)) for n >= 3. - Robert Israel, Aug 28 2014
MAPLE
f := proc(n) option remember; f(n-1) + 2^(ilog2(f(n-1))+ n - 1); end proc:
f(0) := 0:f(1):= 1:
seq(f(n), n=0..60); # updated by Robert Israel, Aug 28 2014
MATHEMATICA
Join[{0}, Accumulate[2^Accumulate[Range[0, 15]]]] (* Harvey P. Dale, Mar 10 2016 *)
PROG
(PARI) a(n)=sum(k=1, n, 2^(k*(k-1)/2)) \\ M. F. Hasler, Aug 28 2014
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Roman Pearce, Oct 17 2010
EXTENSIONS
Prefixed initial term a(0)=0 and simplified definition - M. F. Hasler, Aug 28 2014
STATUS
approved