|
| |
|
|
A005404
|
|
Number of protruded partitions of n with largest part at most 3.
(Formerly M2555)
|
|
1
|
|
|
|
1, 3, 6, 12, 22, 42, 75, 135, 238, 416, 719, 1236, 2107, 3574, 6030, 10130, 16950, 28267, 46993, 77916, 128874, 212701, 350375, 576165, 945984, 1551009, 2539790, 4154212, 6787891, 11081022, 18074324, 29458899, 47981563, 78102314, 127060462
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Ordered structures and partitions, Memoirs of the Amer. Math. Soc., no. 119 (1972).
|
|
|
LINKS
|
|
|
|
FORMULA
|
G.f.: (1-x)^3/Product(1-x-x^i+x^(1+2*i), i=1..3)-1. - Emeric Deutsch, Dec 19 2004
|
|
|
MAPLE
|
G:=(1-x)^3/Product(1-x-x^i+x^(1+2*i), i=1..3)-1: Gser:=series(G, x=0, 39): seq(coeff(Gser, x^n), n=1..37); # Emeric Deutsch, Dec 19 2004
|
|
|
MATHEMATICA
|
Rest@ CoefficientList[Series[(1 - x)^3/Product[1 - x - x^i + x^(1 + 2 i), {i, 3}] - 1, {x, 0, 35}], x] (* Michael De Vlieger, Sep 05 2017 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
