A172033 Number of partitions of n into distinct parts that are 1 or even, i.e., into distinct terms of A004277.

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 10, 10, 12, 12, 15, 15, 18, 18, 22, 22, 27, 27, 32, 32, 38, 38, 46, 46, 54, 54, 64, 64, 76, 76, 89, 89, 104, 104, 122, 122, 142, 142, 165, 165, 192, 192, 222, 222, 256, 256, 296, 296, 340, 340, 390, 390, 448, 448

Offset

0,7

Comments

A000009 repeated: a(n) = A000009(floor(n/2)).

Links

Table of n, a(n) for n=0..67.

Formula

G.f.: (1+q) * Product_{n>=1})(1 + q^(2*n)). [Joerg Arndt, Mar 11 2014]

Example

a(12) = #{12, 10+2, 8+4, 6+4+2} = 4;
a(13) = #{12+1, 10+2+1, 8+4+1, 6+4+2+1} = 4;
a(14) = #{14, 12+2, 10+4, 8+6, 8+4+2} = 5.

Prog

(PARI) N=66; q='q+O('q^N); Vec( (1+q)*prod(n=1, N, 1+q^(2*n)) ) \\ Joerg Arndt, Mar 11 2014

Crossrefs

Cf. A025065.

Sequence in context: A279135 A053266 A112217 * A214131 A229977 A094994

Adjacent sequences: A172030 A172031 A172032 * A172034 A172035 A172036

Keyword

nonn

Author

Reinhard Zumkeller, Jan 23 2010

Status

approved