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Search: id:A005914
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| A005914 |
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Number of points on surface of hexagonal prism: 12n^2 + 2 (coordination sequence for W(2)).
(Formerly M4931)
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+0
4
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| 1, 14, 50, 110, 194, 302, 434, 590, 770, 974, 1202, 1454, 1730, 2030, 2354, 2702, 3074, 3470, 3890, 4334, 4802, 5294, 5810, 6350, 6914, 7502, 8114, 8750, 9410, 10094, 10802, 11534, 12290, 13070, 13874, 14702, 15554, 16430, 17330, 18254
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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For n>=1 a(n) is equal to the number of functions f:{1,2,3,4}->{1,2,...,n,n+1} such that Im(f) contains 2 fixed elements. - Aleksandar M. Janjic and Milan R. Janjic (agnus(AT)blic.net), Feb 24 2007
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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).
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.
Gmelin Handbook of Inorg. and Organomet. Chem., 8th Ed., 1994, TYPIX search code (229) cI2
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
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LINKS
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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.
R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences
R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.
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FORMULA
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Equals binomial transform of [1, 13, 23, 1, -1, 1, -1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 22 2008
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MAPLE
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A005914:=-(z+1)*(z**2+10*z+1)/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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First differences of A005917.
Sequence in context: A043378 A044116 A044497 this_sequence A009960 A009928 A050441
Adjacent sequences: A005911 A005912 A005913 this_sequence A005915 A005916 A005917
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), rwgk(AT)cci.lbl.gov (R.W. Grosse-Kunstleve)
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