Search: id:A005898
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%I A005898 M4616
%S A005898 1,9,35,91,189,341,559,855,1241,1729,2331,3059,3925,4941,6119,7471,
%T A005898 9009,10745,12691,14859,17261,19909,22815,25991,29449,33201,37259,
%U A005898 41635,46341,51389,56791,62559,68705,75241,82179,89531,97309,105525
%N A005898 Centered cube numbers: n^3 + (n+1)^3.
%C A005898 Write the natural numbers in groups: 1; 2,3,4; 5,6,7,8,9; 10,11,12,13,
               14,15,16; ..... and add the groups, i.e. a(n)=sum(i,i=n^2-2(n-1)..n^2). 
               - Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Sep 05 
               2001
%C A005898 The numbers 1, 9, 35, 91, etc. are divisible by 1, 3, 5, 7, etc. Therefore 
               there are no prime numbers in this list. 9 is divisible by 3 and 
               every third number after 9 is also divisible by 3. 35 is divisible 
               by 5 and 7 and every fifth number after 35 is also divisible by 5 
               and every seventh number after 35 is also divisible by 7. This pattern 
               continues indefinitely. [From Howard Berman (howard_berman(AT)hotmail.com), 
               Nov 07 2008]
%C A005898 The running sum of n^3 taken 2 at a time. [From Al Hakanson (hawkuu(AT)gmail.com), 
               May 18 2009]
%D A005898 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005898 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.
%D A005898 T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. 
               (10).
%D A005898 B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral 
               clusters, Inorgan. Chem. 24 (1985), 4545-4558.
%D A005898 D. Zeitlin, A family of Galileo sequences, Amer. Math. Monthly 82 (1975), 
               819-822.
%H A005898 T. D. Noe, <a href="b005898.txt">Table of n, a(n) for n=0..1000</a>
%H A005898 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A005898 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A005898 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CenteredCubeNumber.html">Link to a section of The World of Mathematics.</
               a>
%F A005898 a(n)=2*n^3+9*n^2+15*n+9. Offset 0. a(3)=189. [From Al Hakanson (hawkuu(AT)gmail.com), 
               May 18 2009]
%p A005898 A005898:=(z+1)*(z**2+4*z+1)/(z-1)**4; [Conjectured by S. Plouffe in his 
               1992 dissertation.]
%t A005898 a[n_]:=n^3;lst={};Do[AppendTo[lst,a[n]+a[n+1]],{n,0,6!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Jan 03 2009]
%o A005898 sage: [i^3+(i+1)^3 for i in xrange(0,39)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 03 2008
%Y A005898 1/12*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6, ... gives A049480, A005894, 
               A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, 
               A063492, A005917, A063493, A063494, A063495, A063496.
%Y A005898 Cf. A003215, A000537, A000578 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Jan 03 2009]
%Y A005898 Sequence in context: A033566 A022275 A071398 this_sequence A034957 A002418 
               A118414
%Y A005898 Adjacent sequences: A005895 A005896 A005897 this_sequence A005899 A005900 
               A005901
%K A005898 nonn,easy
%O A005898 0,2
%A A005898 N. J. A. Sloane (njas(AT)research.att.com).

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