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A007588
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Stella octangula numbers: n*(2*n^2 - 1).
(Formerly M4932)
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25
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0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381, 5474, 6735, 8176, 9809, 11646, 13699, 15980, 18501, 21274, 24311, 27624, 31225, 35126, 39339, 43876, 48749, 53970, 59551, 65504, 71841, 78574, 85715, 93276, 101269, 109706, 118599, 127960
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OFFSET
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0,3
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COMMENTS
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Also as a(n)=(1/6)*(12*n^3-6*n), n>0: structured hexagonal anti-diamond numbers (vertex structure 13) (Cf. A005915 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers). - James A. Record (james.record(AT)gmail.com), Nov. 7, 2004.
The only known square stella octangula number for n>1 is a(169) = 169*(2*169^2 - 1) = 9653449 = 3107^2. - Alexander Adamchuk, Jun 02 2008
4*A007588 = A144138(ChebyshevU[3,n]) -- Vladimir Joseph Stephan Orlovsky, Jun 30 2011.
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REFERENCES
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J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 51.
T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Alexander Adamchuk and Vincenzo Librandi, Table of n, a(n) for n = 0..10000 [Alexander Adamchuk computed terms 0 - 169, Jun 02, 2008; Vincenzo Librandi computed the first 10000 terms, Aug 18,2011]
Eric Weisstein's World of Mathematics, Stella Octangula Number.
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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G.f.: (x+10*x^2+x^3)/(1-x)^4.
a(0)=0, a(1)=1, a(2)=14, a(3)=51, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4) [From Harvey P. Dale, Sep 16 2011]
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MATHEMATICA
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Table[ n(2n^2-1), {n, 0, 169} ] - Alexander Adamchuk, Jun 02 2008
CoefficientList[Series[(z^3 + 10 z^2 + z)/(z - 1)^4, {z, 0, 100}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 30 2011 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 14, 51}, 50] (* From Harvey P. Dale, Sep 16 2011 *)
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PROG
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(PARI) a(n)=n*(2*n^2-1)
(MAGMA) [n*(2*n^2 - 1): n in [0..40]]; // Vincenzo Librandi, Aug 18 2011
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CROSSREFS
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Backwards differences give star numbers A003154: A003154(n)=A007588(n)-A007588(n-1).
1/12*t*(n^3-n)+ n for t = 2, 4, 6, ... gives A004006, A006527, A006003, A005900, A004068, A000578, A004126, A000447, A004188, A004466, A004467, A007588, A062025, A063521, A063522, A063523.
Cf. A001653 = Numbers n such that 2*n^2 - 1 is a square.
Sequence in context: A043912 A009961 A059997 * A129025 A113907 A125740
Adjacent sequences: A007585 A007586 A007587 * A007589 A007590 A007591
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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In the formula given in the 1995 Encyclopedia of Integer Sequences, the second 2 should be an exponent.
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STATUS
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approved
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