|
| |
|
|
A008487
|
|
Expansion of (1-x^5 )/(1-x)^5.
|
|
1
|
|
|
|
1, 5, 15, 35, 70, 125, 205, 315, 460, 645, 875, 1155, 1490, 1885, 2345, 2875, 3480, 4165, 4935, 5795, 6750, 7805, 8965, 10235, 11620, 13125, 14755, 16515, 18410, 20445, 22625, 24955, 27440, 30085, 32895, 35875, 39030, 42365, 45885, 49595
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Related to the 4-dimensional cyclotomic lattice Z[zeta_5] (or A_4^{*}).
|
|
|
REFERENCES
|
M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv math.CO/0508136.
|
|
|
LINKS
|
Table of n, a(n) for n=0..39.
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).
|
|
|
FORMULA
|
a(n) is the sum of 5 consecutive tetrahedral (or pyramidal) numbers: C(n+3,3) = (n+1)(n+2)(n+3)/6 = A000292(n) for n>0, a(0) = 1. a(n) = A000292(n-4) + A000292(n-3) + A000292(n-2) + A000292(n-1) + A000292(n) for n>0, a(0) = 1. - Alexander Adamchuk, May 20 2006
binomial(n+7,n+4)+binomial(n+6,n+3)+binomial(n+5,n+2)+binomial(n+4,n+1)+binomial(n+3,n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 03 2006
Equals binomial transform of [1, 4, 6, 4, 1, -1, 1, -1, 1,...]. - Gary W. Adamson, Apr 29 2008
|
|
|
PROG
|
(PARI) Vec((1-x^5)/(1-x)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
|
|
|
CROSSREFS
|
Cf. A000292, A008498, A008531, A222408.
Sequence in context: A005894 A015622 A000750 * A000743 A138779 A090580
Adjacent sequences: A008484 A008485 A008486 * A008488 A008489 A008490
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
STATUS
|
approved
|
| |
|
|
