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Search: id:A001847
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| A001847 |
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Crystal ball sequence for 5-dimensional cubic lattice.
(Formerly M4793 N2045)
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+0
5
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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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 81.
R. G. Stanton and D. D. Cowan, Note on a "square" functional equation, SIAM Rev., 12 (1970), 277-279.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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
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).
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FORMULA
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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
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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
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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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CROSSREFS
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Cf. A013609.
Sequence in context: A002650 A060884 A141935 this_sequence A089764 A023298 A106992
Adjacent sequences: A001844 A001845 A001846 this_sequence A001848 A001849 A001850
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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