|
| |
|
|
A064173
|
|
Number of partitions of n with positive rank.
|
|
6
| |
|
|
0, 1, 1, 2, 3, 5, 6, 10, 13, 19, 25, 35, 45, 62, 80, 106, 136, 178, 225, 291, 366, 466, 583, 735, 912, 1140, 1407, 1743, 2140, 2634, 3214, 3932, 4776, 5807, 7022, 8495, 10225, 12313, 14762, 17696, 21136, 25236, 30030, 35722, 42367, 50216, 59368, 70138
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,4
|
|
|
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-2)-p(n-7)+p(n-15)-... -(-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(18)-p(13)+p(5) =385-101+7 = 291.
|
|
|
MAPLE
| with(combinat): for n from 1 to 30 do P:=partition(n): c:=0: for j from 1 to nops(P) do if P[j][nops(P[j])]>nops(P[j]) then c:=c+1 else c:=c fi od: a[n]:=c: od: seq(a[n], n=1..30); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 11 2004
|
|
|
CROSSREFS
| Cf. A063995.
Cf. A064174.
Sequence in context: A027339 A039837 A039838 * A145724 A039843 A045880
Adjacent sequences: A064170 A064171 A064172 * A064174 A064175 A064176
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 19 2001
|
| |
|
|
