Search: id:A002413
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%I A002413 M4498 N1904
%S A002413 1,8,26,60,115,196,308,456,645,880,1166,1508,1911,2380,2920,3536,4233,
%T A002413 5016,5890,6860,7931,9108,10396,11800,13325,14976,16758,18676,20735,
%U A002413 22940,25296,27808,30481,33320,36330,39516,42883,46436,50180,54120
%N A002413 Heptagonal (or 7-gonal) pyramidal numbers: n(n+1)(5n-2)/6.
%C A002413 Also: the partial sums of A000566, the first term discarded. - R. J. 
               Mathar (mathar(AT)strw.leidenuniv.nl), Mar 19 2008
%D A002413 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002413 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002413 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 A002413 L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 
               256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see 
               vol. 2, p. 2.
%D A002413 A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, 
               p. 194.
%H A002413 T. D. Noe, <a href="b002413.txt">Table of n, a(n) for n=1..1000</a>
%H A002413 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 A002413 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 A002413 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HeptagonalPyramidalNumber.html">Link to a section of The World of 
               Mathematics.</a>
%F A002413 a(n)= n*(n+1)*(5*n-2)/6. G.f.: x*(1+4*x)/(1-x)^4.
%p A002413 A002413:=(1+4*z)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
%t A002413 f[n_]:=5*n+1; s1=s2=0;lst={};Do[a=f[n];s1+=a;s2+=s1;AppendTo[lst,s2],
               {n,0,6!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 
               25 2009]
%Y A002413 Cf. A093562 ((5, 1) Pascal, column m=3).
%Y A002413 Sequence in context: A005897 A111694 A129111 this_sequence A163121 A002901 
               A050471
%Y A002413 Adjacent sequences: A002410 A002411 A002412 this_sequence A002414 A002415 
               A002416
%K A002413 nonn,easy,nice
%O A002413 1,2
%A A002413 N. J. A. Sloane (njas(AT)research.att.com).
%E A002413 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999

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