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Search: id:A008458
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| A008458 |
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Coordination sequence for hexagonal lattice. |
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+0
11
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| 1, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 20 ).
Also the Engel expansion of exp^(1/6); cf. A006784 for the Engel expansion definition - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 03 2002
Coordination sequence for 2-dimensional cyclotomic lattice Z[zeta_6].
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REFERENCES
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M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv math.CO/0508136.
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LINKS
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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).
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))
William A. Stein, The modular forms database
Index entries for sequences related to A2 = hexagonal = triangular lattice
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FORMULA
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G.f.: (1+4*x+x^2)/(1-x)^2.
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MAPLE
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[ seq(6*n, n=0..45) ]; # (except for initial term)
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PROGRAM
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(PARI) a(n)=6*n+(!n)
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CROSSREFS
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A008458(n)=A003215(n)-A003215(n-1), n>0.
Essentially the same as A008588.
Adjacent sequences: A008455 A008456 A008457 this_sequence A008459 A008460 A008461
Sequence in context: A044891 A121827 A126798 this_sequence A008588 A078596 A085129
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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