A105637 a(n) = a(n-2) + a(n-3) - a(n-5).

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

Author

Paul Barry, Apr 16 2005

Keywords

• nonn
• easy

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

• Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1).

Crossrefs

Cf. A000035, A010872, A103221.

Programs

PARI

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

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