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A001847
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Crystal ball sequence for 5-dimensional cubic lattice.
(Formerly M4793 N2045)
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8
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1, 11, 61, 231, 681, 1683, 3653, 7183, 13073, 22363, 36365, 56695, 85305, 124515, 177045, 246047, 335137, 448427, 590557, 766727, 982729, 1244979, 1560549, 1937199, 2383409, 2908411, 3522221, 4235671, 5060441, 6009091, 7095093, 8332863, 9737793, 11326283
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of nodes degree 10 in virtual, optimal chordal graphs of diameter d(G)=n - S. Bujnowski & B. Dubalski (slawb(AT)atr.bydgoszcz.pl), Mar 07 2002
If Y_i (i=1,2,3,4,5) are 2-blocks of a (n+5)-set X then a(n-5) is the number of 10-subsets of X intersecting each Y_i (i=1,2,3,4,5). - Milan R. Janjic (agnus(AT)blic.net), Oct 28 2007
Equals binomial transform of [1, 10, 40, 80, 80, 32, 0, 0, 0,...] where (1, 10, 40, 80, 80, 32) = row 5 of the Chebyshev triangle A013609. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 19 2008
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 81.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. G. Stanton and D. D. Cowan, Note on a "square" functional equation, SIAM Rev., 12 (1970), 277-279.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
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).
Milan Janjic, Two Enumerative Functions
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for crystal ball sequences
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FORMULA
| G.f.: (1+x)^5 /(1-x)^6.
a(n)=(4*n^5+10*n^4+40*n^3+50*n^2+46*n+15)/15 - S. Bujnowski & B. Dubalski (slawb(AT)atr.bydgoszcz.pl), Mar 07 2002
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EXAMPLE
| a(5)=1683, (4*5^5+10*5^4+40*5^3+50*5^2+46*5+15)/15=(12500+6250+5000+230+15)/15=25245/15=1683
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MAPLE
| for n from 1 to k do eval((4*n^5+10*n^4+40*n^3+50*n^2+46*n+15)/15) od;
A001847:=(z+1)**5/(z-1)**6; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| CoefficientList[Series[(z+1)^5/(z-1)^6, {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)
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CROSSREFS
| Cf. A005408, A001844, A001845, A001846, A013609.
Sequence in context: A002650 A060884 A141935 * A089764 A023298 A106992
Adjacent sequences: A001844 A001845 A001846 * A001848 A001849 A001850
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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