Search: id:A003154
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%I A003154 M4893
%S A003154 1,13,37,73,121,181,253,337,433,541,661,793,937,1093,1261,1441,1633,
%T A003154 1837,2053,2281,2521,2773,3037,3313,3601,3901,4213,4537,4873,5221,
%U A003154 5581,5953,6337,6733,7141,7561,7993,8437,8893,9361,9841,10333,10837
%N A003154 Centered 12-gonal numbers. Also star numbers: 6n(n-1) + 1.
%C A003154 Except for the first term, numbers n to the first diagonal to A162245 
               (13,37,73,121,..) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Sep 28 2009]
%C A003154 Except for the first term, a(n)=12*n+a(n-1), (with a(1)=13) [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
%D A003154 M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, 
               NY, 1988, p. 20.
%D A003154 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003154 T. D. Noe, <a href="b003154.txt">Table of n, a(n) for n=1..1000</a>
%H A003154 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 A003154 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 A003154 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               StarNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A003154 <a href="Sindx_Ce.html#CENTRALCUBE">Index entries for sequences related 
               to centered polygonal numbers</a>
%F A003154 G.f.: (x+10*x^2+x^3)/(1-x)^3.
%F A003154 a(n)= 1 + (sum(12*n)). E.g. a(2)=37 because 1+ 12*0 + 12*1 + 12*2 =37. 
               - Xavier Acloque, Oct 06 2003
%F A003154 a(n) = numerator in B_2(x) = (1/2)x^2 - (1/2)x + 1/12 = Bernoulli polynomial 
               of degree 2. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 30 2005
%F A003154 Binomial transform of [1, 12, 12, 0, 0, 0,...]; Narayana transform (A001263) 
               of [1, 12, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Dec 29 2007
%p A003154 A003154:=-(1+10*z+z**2)/(z-1)**3; [S. Plouffe in his 1992 dissertation.]
%t A003154 lst={};Do[AppendTo[lst, LegendreP[2, n]], {n, 1, 10^3, 2}];lst [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]
%o A003154 (Other) sage: [6* bernoulli_polynomial(n,2) for n in xrange(1, 44)]# 
               [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2009]
%Y A003154 Cf. A007588, A049598, A003215.
%Y A003154 Cf. A001263.
%Y A003154 Sequence in context: A049742 A113601 A158864 this_sequence A083577 A155285 
               A155262
%Y A003154 Adjacent sequences: A003151 A003152 A003153 this_sequence A003155 A003156 
               A003157
%K A003154 nonn,easy,nice
%O A003154 1,2
%A A003154 N. J. A. Sloane (njas(AT)research.att.com).
%E A003154 More terms from Michael Somos

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