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A005914
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Number of points on surface of hexagonal prism: 12n^2 + 2 for n>0 (coordination sequence for W(2)).
(Formerly M4931)
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7
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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, 19202, 20174, 21170
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
Equals binomial transform of [1, 13, 23, 1, -1, 1, -1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 22 2008
First bisection of A005918. After 1, all terms are in A000408 (see Formula section). - Bruno Berselli, Feb 07 2012
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REFERENCES
| Gmelin Handbook of Inorg. and Organomet. Chem., 8th Ed., 1994, TYPIX search code (229) cI2
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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.
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 to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: (1+x)*(1+10*x+x^2)/(1-x)^3. - S. Plouffe (see MAPLE line)
a(n) = (2n-1)^2+(2n)^2+(2n+1)^2 for n>0. - Bruno Berselli, Jan 30 2012
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MAPLE
| A005914:=-(z+1)*(z**2+10*z+1)/(z-1)**3; [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[If[n == 0, 1, 12*n^2 + 2], {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)
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PROG
| (PARI) a(n)=12*n^2+2 \\ Charles R Greathouse IV, Jan 31 2012
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CROSSREFS
| First differences of A005917.
Cf. A206399.
Sequence in context: A043378 A044116 A044497 * A009960 A009928 A050441
Adjacent sequences: A005911 A005912 A005913 * A005915 A005916 A005917
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KEYWORD
| nonn,easy,nice,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), rwgk(AT)cci.lbl.gov (R.W. Grosse-Kunstleve)
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