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Search: id:A003154
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| A003154 |
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Centered 12-gonal numbers. Also star numbers: 6n(n-1) + 1.
(Formerly M4893)
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+0
18
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| 1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, 1093, 1261, 1441, 1633, 1837, 2053, 2281, 2521, 2773, 3037, 3313, 3601, 3901, 4213, 4537, 4873, 5221, 5581, 5953, 6337, 6733, 7141, 7561, 7993, 8437, 8893, 9361, 9841, 10333, 10837
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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]
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]
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REFERENCES
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M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 20.
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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T. D. Noe, Table of n, a(n) for n=1..1000
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.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to centered polygonal numbers
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FORMULA
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G.f.: (x+10*x^2+x^3)/(1-x)^3.
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
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
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
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MAPLE
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A003154:=-(1+10*z+z**2)/(z-1)**3; [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
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lst={}; Do[AppendTo[lst, LegendreP[2, n]], {n, 1, 10^3, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]
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PROGRAM
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(Other) sage: [6* bernoulli_polynomial(n, 2) for n in xrange(1, 44)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2009]
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CROSSREFS
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Cf. A007588, A049598, A003215.
Cf. A001263.
Sequence in context: A049742 A113601 A158864 this_sequence A083577 A155285 A155262
Adjacent sequences: A003151 A003152 A003153 this_sequence A003155 A003156 A003157
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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 (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Michael Somos
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