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Search: id:A001848
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| A001848 |
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Crystal ball sequence for 6-dimensional cubic lattice.
(Formerly M4904 N2102)
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+0
1
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| 1, 13, 85, 377, 1289, 3653, 8989, 19825, 40081, 75517, 134245, 227305, 369305, 579125, 880685, 1303777, 1884961, 2668525, 3707509, 5064793, 6814249, 9041957, 11847485, 15345233, 19665841
(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 of degree 12 in virtual, optimal chordal graphs of diameter d(G)=n - S. Bujnowski & B. Dubalski (slawb(AT)atr.bydgoszcz.pl), Nov 25 2002
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REFERENCES
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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
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.
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).
Index entries for crystal ball sequences
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FORMULA
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G.f.: (1+x)^6 /(1-x)^7.
a(n) = 4/45*n^6+4/15*n^5+14/9*n^4+8/3*n^3+196/45*n^2+46/15*n+1 - S. Bujnowski & B. Dubalski (slawb(AT)atr.bydgoszcz.pl), Nov 25 2002
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MAPLE
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for n from 1 to k do eval(4/45*n^6+4/15*n^5+14/9*n^4+8/3*n^3+196/45*n^2+46/15*n+1); od;
A001848:=-(z+1)**6/(z-1)**7; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A101102 A142085 A010025 this_sequence A055843 A003764 A082036
Adjacent sequences: A001845 A001846 A001847 this_sequence A001849 A001850 A001851
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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