

A181388


a(n) = Sum_{k=1..n} 2^T(k1), where T = A000217 are the triangular numbers 0, 1, 3, 6, 10, ... . For n=0 we have the empty sum equal to 0.


4



0, 1, 3, 11, 75, 1099, 33867, 2131019, 270566475, 68990043211, 35253362132043, 36064050381096011, 73823040345219302475, 302305277944002512979019, 2476182383848704552311227467, 40567295389687189552446813799499, 1329268563080305560093359507094144075
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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 n1 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(n1) + 2*(a(n1)  a(n2))^2/(a(n2)  a(n3)) for n >= 3.  Robert Israel, Aug 28 2014


MAPLE

f := proc(n) option remember; f(n1) + 2^(ilog2(f(n1))+ 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*(k1)/2)) \\ M. F. Hasler, Aug 28 2014


CROSSREFS

Cf. A000217, A006125.
Sequence in context: A054461 A203772 A290025 * A196691 A197064 A117765
Adjacent sequences: A181385 A181386 A181387 * A181389 A181390 A181391


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



