OFFSET
1,3
COMMENTS
Starting at a(2), this is column 2 of Table 1 of the Donald M. Davis paper, p.32. - Jonathan Vos Post, Jul 17 2008
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n=1..1000
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197.
J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II
L. Babai, On the length of subgroup chains in the symmetric group, Commun. Algebra, 14 (1986), 1729-1736.
P. J. Cameron, M. Gadouleau, J. D. Mitchell, Y. Peresse, Chains of subsemigroups, arXiv preprint arXiv:1501.06394 [math.GR], 2015.
Peter J. Cameron; Ron Solomon; Alexandre Turull, Chains of subgroups in symmetric groups, J. Algebra 127 (1989), no. 2, 340-352.
Donald M. Davis, Divisibility by 2 and 3 of certain Stirling numbers, arXiv:0807.2629 [math.NT], Jul 16, 2008.
FORMULA
a(n) = ceiling(3n/2) - b(n) - 1, where b(n) = # 1's in binary expansion of n (A000120).
G.f.: 1/(1-x) * (-1/(1-x^2) + Sum(k>=0, x^2^k/(1-x^2^k))). - Ralf Stephan, Apr 13 2002
MAPLE
MATHEMATICA
a[n_] := Ceiling[ 3n/2 ] - Count[ IntegerDigits[n, 2], 1] - 1; Table[ a[n], {n, 1, 70}] (* Jean-François Alcover, Jan 19 2012, after formula *)
Table[Ceiling[(3n)/2]-DigitCount[n, 2, 1]-1, {n, 70}] (* Harvey P. Dale, Nov 20 2021 *)
PROG
(PARI) vector(70, n, ceil(3*n/2) - hammingweight(n) - 1) \\ Joerg Arndt, May 16 2016
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
STATUS
approved