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Search: id:A069039
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| A069039 |
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G.f.: x(1+x)^5/(1-x)^7. |
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+0
4
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| 0, 1, 12, 73, 304, 985, 2668, 6321, 13504, 26577, 48940, 85305, 142000, 227305, 351820, 528865, 774912, 1110049, 1558476, 2149033, 2915760, 3898489, 5143468, 6704017, 8641216, 11024625, 13933036, 17455257, 21690928, 26751369, 32760460
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Figurate numbers based on the 6-dimensional regular convex polytope called the 6-dimensional cross-polytope, or 6-dimensional hyperoctahedron, which is represented by the Schlaefli symbol {3, 3, 3, 3, 4}. It is the dual of the 6-dimensional hypercube. Kim asserts that every nonnegative integer can be represented by the sum of no more than 19 of these 6-crosspolytope numbers. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Nov 16 2004
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REFERENCES
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H. S. M. Coxeter, Regular Polytopes, New York: Dover, 1973.
J. V. Post, "4-Dimensional Jonathan numbers: polytope numbers and Centered polytope numbers of Higher Than 3 Dimensions", Draft 1.5 of 9 a.m., 12 March 2004, circulated by e-mail.
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LINKS
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H. K. Kim, "On Regular polytope numbers".
J. V. Post, Table of polytope numbers, Sorted, Through 1,000,000.
J. V. Post, Math Pages.
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FORMULA
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Recurrence: a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7).
a(n) = 6-crosspolytope(n) = (n^2)*(2*n^4 + 20*n^2 + 23 )/45. E. g. a(12) = 142000 because (12^2)*(2*12^4 + 20*12^2 + 23 )/45. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Nov 16 2004
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MAPLE
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al:=proc(s, n) binomial(n+s-1, s); end; be:=proc(d, n) local r; add( (-1)^r*binomial(d-1, r)*2^(d-1-r)*al(d-r, n), r=0..d-1); end; [seq(be(6, n), n=0..100)];
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CROSSREFS
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Cf. A000332, A014820, A005900, A069038, A099193, A099195.
Adjacent sequences: A069036 A069037 A069038 this_sequence A069040 A069041 A069042
Sequence in context: A120783 A103475 A024014 this_sequence A041270 A055912 A064121
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 03 2002
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