A026927 Number of partitions of n into an even number of parts, the greatest being 3; also, a(n+5) = number of partitions of n+2 into an odd number of parts, each <= 3.

0, 0, 0, 1, 1, 2, 1, 3, 3, 5, 4, 7, 6, 9, 8, 12, 11, 15, 13, 18, 17, 22, 20, 26, 24, 30, 28, 35, 33, 40, 37, 45, 43, 51, 48, 57, 54, 63, 60, 70, 67, 77, 73, 84, 81, 92, 88, 100, 96, 108, 104, 117

Offset

1,6

Links

Table of n, a(n) for n=1..52.

Formula

a(n) + A026923(n) = A069905(n). - R. J. Mathar, Aug 22 2019

Conjectures from Colin Barker, Sep 01 2019: (Start)

G.f.: x^4*(1 + x^2 - x^3 + x^4) / ((1 - x)^3*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)).

a(n) = a(n-1) + a(n-4) - a(n-5) + a(n-6) - a(n-7) - a(n-10) + a(n-11) for n>11.

(End)

Example

Figure 1: The partitions of n into 3 parts for n = 3, 4, ...
                                                          1+1+8
                                                   1+1+7  1+2+7
                                                   1+2+6  1+3+6
                                            1+1+6  1+3+5  1+4+5
                                     1+1+5  1+2+5  1+4+4  2+2+6
                              1+1+4  1+2+4  1+3+4  2+2+5  2+3+5
                       1+1+3  1+2+3  1+3+3  2+2+4  2+3+4  2+4+4
         1+1+1  1+1+2  1+2+2  2+2+2  2+2+3  2+3+3  3+3+3  3+3+4    ...
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  n  |     3      4      5      6      7      8      9     10      ...
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a(n) |     0      1      1      2      1      3      3      5      ...
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Crossrefs

3rd column of A026921.

Cf. A026923, A309683, A309684, A309685, A309686, A309687, A309688, A309689, A309690, A309692, A309694.

Sequence in context: A152993 A178133 A343379 * A240863 A288005 A237832

Adjacent sequences: A026924 A026925 A026926 * A026928 A026929 A026930

Keyword

nonn

Author

Clark Kimberling

Status

approved