OFFSET
0,3
COMMENTS
A 17-divide version of A084230.
The Harborth : f(2^k)=3^k suggests that a family of sequences of the form: f(2^k)=Prime[n]^k There does indeed seem to be an infinite family of such functions.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
H. Harborth, Number of Odd Binomial Coefficients, Proc. Amer. Math. Soc. 62, 19-22, 1977.
Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, pp. 27, 33.
Eric Weisstein's World of Mathematics, Stolarsky-Harborth Constant
FORMULA
a(n) = Sum_{k=0..n-1} 16^wt(k), where wt = A000120. - Mike Warburton, Mar 22 2019
MAPLE
a:=proc(n) if n=0 then 0 elif n=1 then 1 elif n mod 2 = 0 then 17*a(n/2) else 16*a((n-1)/2)+a((n+1)/2) fi end: seq(a(n), n=0..38);
MATHEMATICA
b[0] := 0; b[1] := 1; b[n_?EvenQ] := b[n] = 17*b[n/2]; b[n_?OddQ] := b[n] = 16*b[(n - 1)/2] + b[(n + 1)/2]; a = Table[b[n], {n, 1, 25}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Mar 15 2006
EXTENSIONS
Edited by N. J. A. Sloane, Apr 16 2005
STATUS
approved