|
Search: id:A117957
|
|
|
| A117957 |
|
Number of partitions of n into parts larger than 1 and congruent to 1 mod 4. |
|
+0
1
|
|
| 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 2, 1, 2, 3, 3, 2, 2, 4, 4, 3, 3, 5, 6, 5, 4, 6, 8, 7, 6, 8, 10, 10, 9, 10, 13, 13, 12, 14, 17, 18, 16, 18, 22, 23, 22, 23, 28, 31, 29, 30, 36, 39, 39, 39, 45, 51, 50, 51, 57, 64, 65, 65, 73, 81, 83, 84, 91, 102, 106, 106
(list; graph; listen)
|
|
|
OFFSET
|
0,19
|
|
|
COMMENT
|
Also number of partitions of n such that 2k and 2k+1 occur with the same multiplicities. Example: a(26)=3 because we have [11,10,3,2], [9,8,5,4] and [7,7,6,6]. It is easy to find a bijection between these partitions and those described in the definition.
|
|
FORMULA
|
G.f.=1/product(1-x^(4i+1), i=1..infinity).
|
|
EXAMPLE
|
a(26)=3 because we have [21,5],[17,9] and [13,13].
|
|
MAPLE
|
g:=1/product(1-x^(4*i+1), i=1..50): gser:=series(g, x=0, 93): seq(coeff(gser, x, n), n=0..88);
|
|
CROSSREFS
|
Cf. A035451, A035462.
Sequence in context: A089641 A086995 A135230 this_sequence A139632 A145704 A145705
Adjacent sequences: A117954 A117955 A117956 this_sequence A117958 A117959 A117960
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 05 2006
|
|
|
Search completed in 0.002 seconds
|
