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A105637
a(n) = a(n-2) + a(n-3) - a(n-5).
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
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*(i-1) to every term of the i-th 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
FORMULA
G.f.: x*(1+2*x)/((1-x^2)*(1-x^3)).
a(n) = Sum_{k=0..n} (k mod 3)*(1-(-1)^(n+k-1))/2}.
a(n) = Sum_{k=0..floor(n/2)} (n-2k mod 3).
a(n) = 1 + floor(n/2) - [3 divides n]. - Ralf Stephan, Nov 15 2010
a(n) = A103221(n-1) + 2*A103221(n-2). - 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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 16 2005
STATUS
approved