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A121659 Number of partitions of n into parts with at most one part not greater than 2. 2
1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 15, 20, 25, 32, 40, 51, 63, 79, 97, 121, 148, 182, 221, 271, 328, 398, 479, 579, 694, 834, 995, 1190, 1415, 1684, 1995, 2366, 2793, 3298, 3881, 4569, 5360, 6288, 7355, 8603, 10037, 11705, 13619, 15842, 18388, 21333, 24703 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The number of partitions of n that have the first part at least thrice larger than the second part. Example: a(8) = #{8, 7+1, 6+2, 6+1+1, 5+1+1+1, 4+1+1+1+1, 3+1+1+1+1+1}=7. [Mircea Merca, Jul 24 2011]

LINKS

Table of n, a(n) for n=1..51.

Mircea Merca, Fast algorithm for generating ascending compositions, arXiv:1903.10797 [math.CO], 2019.

FORMULA

a(n) = A121081(n) - A008483(n-3) for n>2.

a(n) = p(n) - p(n-2) - p(n-3) + p(n-5) where p(n) = A000041(n). See Merca p. 6. - Michel Marcus, Mar 27 2019

EXAMPLE

a(8) = #{8,7+1,6+2,5+3,4+4,4+3+1,3+3+2} = 7;

a(9) = #{9,8+1,7+2,6+3,5+4,5+3+1,4+4+1,4+3+2,3+3+3} = 9.

CROSSREFS

Cf. A027336, A008483, A121081, A000041.

Sequence in context: A003413 A100853 A174065 * A096814 A039861 A039877

Adjacent sequences:  A121656 A121657 A121658 * A121660 A121661 A121662

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 14 2006

STATUS

approved

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Last modified October 27 19:59 EDT 2020. Contains 338036 sequences. (Running on oeis4.)