|
| |
|
|
A008795
|
|
Molien series for 3-dimensional group [2,n]+ = 22n.
|
|
5
| |
|
|
1, 0, 3, 1, 6, 3, 10, 6, 15, 10, 21, 15, 28, 21, 36, 28, 45, 36, 55, 45, 66, 55, 78, 66, 91, 78, 105, 91, 120, 105, 136, 120, 153, 136, 171, 153, 190, 171, 210, 190, 231, 210, 253, 231, 276, 253, 300, 276, 325, 300
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| a(n-3) = number of ordered triples of positive integers which are the side lengths of a nondegenerate triangle of perimeter n. - Rob Pratt (Rob.Pratt(AT)sas.com), Jul 12 2004
a(n) is the number of ways to distribute n identical objects into 3 distinguishable bins so that no bin contains an absolute majority of objects. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 17 2010]
Contribution from Omar E. Pol, Feb 05 2012 (Start:)
Also positive terms of A000217 and A000217 interleaved.
For the connection with the generalized polygonal numbers and some other sequences see A194801. (End)
|
|
|
REFERENCES
| Ira Rosenholtz, Problem 1584, Mathematics Magazine, Vol. 72 (1999), p. 408.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for Molien series
|
|
|
FORMULA
| The signed version with g.f. (1-x^3)/(1-x^2)^3 is the inverse binomial transform of A084861. - Paul Barry (pbarry(AT)wit.ie), Jun 12 2003
a(n) = binom(n/2+2, 2) for n even, binom((n+1)/2, 2) for n odd - Rob Pratt (Rob.Pratt(AT)sas.com), Jul 12 2004
a(n-2) interleaves n(n+1)/2 and n(n-1)/2. G.f.: (1-x+x^2)/((1+x)^2(1-x)^3)); a(n)=(2n^2+6n+7)/16+3(2n+3)(-1)^n/16. - Paul Barry (pbarry(AT)wit.ie), Jul 29 2004
a(n) = n*(n+1)/2, n = +- 1, +- 2... - Omar E. Pol, Feb 05 2012
|
|
|
MATHEMATICA
| Table[If[EvenQ[n], Binomial[n/2+2, 2], Binomial[(n+1)/2, 2]], {n, 0, 49}]
CoefficientList[ Series[(1 + x^3)/(1 - x^2)^3, {x, 0, 50}], x] (* Robert G. Wilson v, Feb 05 2012 *)
|
|
|
PROG
| (MAGMA) [(2*n^2+6*n+7)/16+3*(2*n+3)*(-1)^n/16: n in [0..60] ]; // Vincenzo Librandi, Aug 21 2011
|
|
|
CROSSREFS
| Cf. A005044.
First differences of A053307.
Sequence in context: A185628 A158822 A121443 * A165188 A132180 A126191
Adjacent sequences: A008792 A008793 A008794 * A008796 A008797 A008798
|
|
|
KEYWORD
| nonn,easy,changed
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
