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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 (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*(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

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)/((1-x^2)*(1-x^3)); a(n)=sum{k=0..n, mod(k, 3)*(1-(-1)^(n+k-1))/2}; a(n)=sum{k=0..floor(n/2), mod(n-2k, 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 A303974

Adjacent sequences:  A105634 A105635 A105636 * A105638 A105639 A105640

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 16 2005

STATUS

approved

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Last modified January 22 06:03 EST 2021. Contains 340360 sequences. (Running on oeis4.)