|
| |
|
|
A008732
|
|
Molien series for 3-dimensional group [2,n] = *22n.
|
|
8
| |
|
|
1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, 30, 34, 38, 42, 46, 50, 55, 60, 65, 70, 75, 81, 87, 93, 99, 105, 112, 119, 126, 133, 140, 148, 156, 164, 172, 180, 189, 198, 207, 216, 225, 235, 245, 255, 265
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| Brian OSullivan and Thomas Busch, Spontaneous emission in ultra-cold spin-polarised anisotropic Fermi seas, arXiv 0810.0231v1 [quant-ph], 2008. [Eq 8a, lambda=5]
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 188
Index entries for Molien series
|
|
|
FORMULA
| a(n) = floor( (n+3)*(n+4)/10 ) = (n+2)*(n+5)/10 + b(n)/5 where b(n) = A010891(n-2)+2*A092202(n-1) = 0, 1, 1, 0, -2,.. with period length 5.
G.f.: 1/((1-x)^2*(1-x^5)).
a(n)=a(n-5)+n+1. - Paul Barry (pbarry(AT)wit.ie), Jul 14 2004
a(n) = sum(floor(j/5), {j,0,n+5}), a(n-5) = (1/2)floor(n/5)*(2n-3-5*floor(n/5)) [From Mitch Harris (maharri(AT)gmail.com), Sep 08 2008]
|
|
|
MAPLE
| A092202 := proc(n) op(1+(n mod 5), [0, 1, 0, -1, 0]) ; end proc:
A010891 := proc(n) op(1+(n mod 5), [1, -1, 0, 0, 0]) ; end proc:
A008732 := proc(n) (n+2)*(n+5)/10+(A010891(n-1)+2*A092202(n-1))/5 ; end proc:
|
|
|
MATHEMATICA
| s=0; lst={}; Do[AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n]; AppendTo[lst, s+=n], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 14 2010]
|
|
|
PROG
| (MAGMA) [Floor( (n+3)*(n+4)/10 ): n in [0..60] ]; // Vincenzo Librandi, Aug 21 2011
|
|
|
CROSSREFS
| Sequence in context: A024926 A051532 A135785 * A130520 A005706 A173345
Adjacent sequences: A008729 A008730 A008731 * A008733 A008734 A008735
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
