A172033 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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;