|
| |
|
|
A000715
|
|
Number of partitions of n, with three kinds of 1,2 and 3 and two kinds of 4,5,6,....
(Formerly M2786 N1121)
|
|
0
| |
|
|
1, 3, 9, 22, 50, 104, 208, 394, 724, 1286, 2229, 3769, 6253, 10176, 16303, 25723, 40055, 61588, 93647, 140875, 209889, 309846, 453565, 658627, 949310, 1358589, 1931464, 2728547, 3831654, 5350119, 7430158, 10265669
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 122.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| N. J. A. Sloane, Transforms
|
|
|
FORMULA
| EULER transform of 3, 3, 3, 2, 2, 2, 2, 2...
G.f.=1/[(1-x)(1-x^2)(1-x^3)product((1-x^k)^2, k=1..infinity)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006
|
|
|
EXAMPLE
| a(2)=9 because we have 2, 2', 2", 1+1, 1'+1', 1"+1", 1+1', 1+1", 1'+1".
|
|
|
MAPLE
| g:=1/((1-x)*(1-x^2)*(1-x^3)*product((1-x^k)^2, k=1..40)): gser:=series(g, x=0, 40): seq(coeff(gser, x, n), n=0..31); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006
|
|
|
CROSSREFS
| Sequence in context: A187053 A001937 A086817 * A034505 A143099 A160462
Adjacent sequences: A000712 A000713 A000714 * A000716 A000717 A000718
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Extended with formula from Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.
|
| |
|
|
