Search: id:A007588
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%I A007588 M4932
%S A007588 0,1,14,51,124,245,426,679,1016,1449,1990,2651,3444,4381,5474,6735,
%T A007588 8176,9809,11646,13699,15980,18501,21274,24311,27624,31225,35126,
%U A007588 39339,43876,48749,53970,59551,65504,71841,78574,85715,93276,101269
%N A007588 Stella octangula numbers: n(2n^2 - 1).
%C A007588 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.
%C A007588 The only known square stella octangula number for n>1 is a(169) = 169*(2*169^2 
               - 1) = 9653449 = 3107^2. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Jun 02 2008
%D A007588 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007588 J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 
               1996, p. 51.
%D A007588 T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. 
               (11).
%H A007588 Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2008, <a href="b007588.txt">
               Table of n, a(n) for n = 0..169</a>
%H A007588 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A007588 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               StellaOctangulaNumber.html">Link to a section of The World of Mathematics.</
               a>
%F A007588 G.f.: (x+10*x^2+x^3)/(1-x)^4.
%t A007588 Table[ n(2n^2-1), {n,0,169} ] - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Jun 02 2008
%o A007588 (PARI) a(n)=n*(2*n^2-1)
%Y A007588 Backwards differences give star numbers A003154: A003154(n)=A007588(n)-A007588(n-1).
%Y A007588 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.
%Y A007588 Cf. A001653 = Numbers n such that 2*n^2 - 1 is a square.
%Y A007588 Sequence in context: A043912 A009961 A059997 this_sequence A129025 A113907 
               A125740
%Y A007588 Adjacent sequences: A007585 A007586 A007587 this_sequence A007589 A007590 
               A007591
%K A007588 nonn,easy,nice
%O A007588 0,3
%A A007588 N. J. A. Sloane (njas(AT)research.att.com).
%E A007588 In the formula given in the 1995 Encyclopedia of Integer Sequences, the 
               second 2 should be an exponent.

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