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A064174 Number of partitions of n with nonnegative rank. 6
1, 1, 2, 3, 4, 6, 9, 12, 17, 23, 31, 42, 56, 73, 96, 125, 161, 207, 265, 336, 426, 536, 672, 840, 1046, 1296, 1603, 1975, 2425, 2970, 3628, 4417, 5367, 6503, 7861, 9482, 11412, 13702, 16423, 19642, 23447, 27938, 33231, 39453, 46767, 55342, 65386, 77135 (list; graph; refs; listen; history; internal format)
OFFSET

1,3

COMMENTS

The rank of a partition is the largest summand minus the number of summands.

FORMULA

a(n) = (A000041(n)+A047993(n))/2.

a(n) = p(n-1)-p(n-5)+p(n-12)-... -(-1)^k*p(n-(3*k^2-k)/2)+..., where p() is A000041(). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 04 2004

EXAMPLE

a(20) = p(19)-p(15)+p(8) =490-176+22 = 336.

CROSSREFS

Cf. A063995.

Cf. A064173.

Row sums of triangle A105806.

Sequence in context: A035992 A036003 A027338 * A062121 A094995 A018591

Adjacent sequences:  A064171 A064172 A064173 * A064175 A064176 A064177

KEYWORD

nonn

AUTHOR

Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 20 2001

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Last modified February 13 16:42 EST 2012. Contains 205523 sequences.