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Search: id:A100157
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| A100157 |
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Structured rhombic dodecahedral numbers (vertex structure 9). |
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+0
6
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| 1, 14, 55, 140, 285, 506, 819, 1240, 1785, 2470, 3311, 4324, 5525, 6930, 8555, 10416, 12529, 14910, 17575, 20540, 23821, 27434, 31395, 35720, 40425, 45526, 51039, 56980, 63365, 70210, 77531, 85344
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also structured triakis octahedral numbers (vertex structure 9) (Cf. A100171 = alternate vertex); and structured heptagonal anti-prism numbers (Cf. A100185 = structured anti-prisms).
If Y is a 2-subset of a 2n-set X then, for n>=2, a(n-1) is the number of 4-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Nov 18 2007
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LINKS
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Milan Janjic, Two Enumerative Functions
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FORMULA
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a(n)=(1/6)*(16*n^3-12*n^2+2*n)
a(n) = n*(2*n-1)*(4*n-1)/3 = A000330(2*n-1). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 06 2009]
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MAPLE
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with(combstruct):ZL:=[st, {st=Prod(left, right), left=Set(U, card=r), right=Set(U, card=r), U=Sequence(Z, card>=1)}, unlabeled]: subs(r=1, stack): seq(count(subs(r=2, ZL), size=m*4), m=1..32) ; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 02 2008
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CROSSREFS
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Cf. A005915 = alternate vertex; A100145 for more on structured polyhedral numbers.
Sequence in context: A114012 A140784 A022285 this_sequence A144555 A115129 A067326
Adjacent sequences: A100154 A100155 A100156 this_sequence A100158 A100159 A100160
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KEYWORD
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easy,nonn
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AUTHOR
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James A. Record (james.record(AT)gmail.com). Nov 07, 2004.
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