

A105637


a(n) = a(n2)+a(n3)a(n5).


8



0, 1, 2, 1, 3, 3, 3, 4, 5, 4, 6, 6, 6, 7, 8, 7, 9, 9, 9, 10, 11, 10, 12, 12, 12, 13, 14, 13, 15, 15, 15, 16, 17, 16, 18, 18, 18, 19, 20, 19, 21, 21, 21, 22, 23, 22, 24, 24, 24, 25, 26, 25, 27, 27, 27, 28, 29, 28, 30, 30, 30, 31, 32, 31, 33, 33, 33, 34, 35, 34, 36, 36, 36, 37, 38, 37
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

a(n+6) = a(n) + 3; convolution of A000035(n) with A010872(n).  Reinhard Zumkeller, Mar 08 2009
Let B be the periodic sequence that repeats (1,2,1,3,3,3,4,5,4,6,6,6). Then the sequence a(1), a(2),... is obtained by adding 6*(i1) to every term of the ith period of B..  Vladimir Shevelev, May 31 2011
Also for n > 0: number of partitions of n into parts 1 or 2 with distinct multiplicities, cf. A211858, A098859.  Reinhard Zumkeller, Dec 27 2012


LINKS

Table of n, a(n) for n=0..75.
Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,1).


FORMULA

G.f.: x*(1+2*x)/((1x^2)*(1x^3)); a(n)=sum{k=0..n, mod(k, 3)*(1(1)^(n+k1))/2}; a(n)=sum{k=0..floor(n/2), mod(n2k, 3)}.
a(n) = 1+floor(n/2)[3 divides n].  Ralf Stephan, Nov 15 2010.
a(n) = A103221(n1)+2*A103221(n2).  R. J. Mathar, Jun 30 2011
a(n) = floor(n/2)+floor((n+2)/3)floor(n/3).  Mircea Merca, May 20 2013


PROG

(PARI) a(n)=1+floor(n/2)if(n%3==0, 1, 0)


CROSSREFS

Cf. A174257.  Vladimir Shevelev, May 31 2011
Sequence in context: A302395 A110425 A174257 * A029161 A035384 A360033
Adjacent sequences: A105634 A105635 A105636 * A105638 A105639 A105640


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Apr 16 2005


STATUS

approved



