|
Search: id:A096000
|
|
|
| A096000 |
|
Cupolar numbers: (1/3)*(n+1)*(5*n^2+7*n+3). |
|
+0
6
|
|
| 1, 10, 37, 92, 185, 326, 525, 792, 1137, 1570, 2101, 2740, 3497, 4382, 5405, 6576, 7905, 9402, 11077, 12940, 15001, 17270, 19757, 22472, 25425, 28626, 32085, 35812, 39817, 44110, 48701, 53600, 58817, 64362, 70245, 76476, 83065, 90022, 97357, 105080, 113201
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Number of equal balls that will fill a triangular cupola, formed by splitting a cuboctahedron along one of its four "equilateral" hexagons.
Also as a(n)=(1/6)*(10*n^3-6*n^2+10*n), n>0: structured pentagonal anti-prism numbers (Cf. A100185 = structured anti-prisms); and structured tetragonal anti-diamond numbers (vertex structure 7) (Cf. A000447 = alternate vertex; A100188 = structured anti-diamonds). Cf. A100145 for more on structured numbers. - James A. Record (james.record(AT)gmail.com), Nov. 7, 2004.
|
|
REFERENCES
|
H. S. M. Coxeter, Polyhedral numbers, pp. 25-35 of R. S. Cohen, J. J. Stachel and M. W. Wartofsky, eds., For Dirk Struik: Scientific, historical and political essays in honor of Dirk J. Struik, Reidel, Dordrecht, 1974.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..1000
|
|
FORMULA
|
Equals (1/2)*(Q(n) + 3n^2 + 3n + 1), where Q(n) are the cuboctahedral numbers, A005902.
G.f.: (1+6x+3x^2)/(1-x)^4; - Paul Barry (pbarry(AT)wit.ie), Oct 28 2006
|
|
CROSSREFS
|
Sequence in context: A089222 A139242 A139236 this_sequence A047672 A048480 A116970
Adjacent sequences: A095997 A095998 A095999 this_sequence A096001 A096002 A096003
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), in memory of Harold Scott MacDonald Coxeter [Feb 09 1907 - Mar 31 2003], May 08 2004
|
|
|
Search completed in 0.002 seconds
|
