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A096000
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Cupolar numbers: (1/3)*(n+1)*(5*n^2+7*n+3).
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6
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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.
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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.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
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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
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CROSSREFS
| Sequence in context: A089222 A139242 A139236 * A047672 A200872 A048480
Adjacent sequences: A095997 A095998 A095999 * A096001 A096002 A096003
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KEYWORD
| nonn
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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
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