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Search: id:A002413
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| A002413 |
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Heptagonal (or 7-gonal) pyramidal numbers: n(n+1)(5n-2)/6.
(Formerly M4498 N1904)
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+0
9
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| 1, 8, 26, 60, 115, 196, 308, 456, 645, 880, 1166, 1508, 1911, 2380, 2920, 3536, 4233, 5016, 5890, 6860, 7931, 9108, 10396, 11800, 13325, 14976, 16758, 18676, 20735, 22940, 25296, 27808, 30481, 33320, 36330, 39516, 42883, 46436, 50180, 54120
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also: the partial sums of A000566, the first term discarded. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 19 2008
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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.
A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 194.
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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.
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FORMULA
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a(n)= n*(n+1)*(5*n-2)/6. G.f.: x*(1+4*x)/(1-x)^4.
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MAPLE
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A002413:=(1+4*z)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A093562 ((5, 1) Pascal, column m=3).
Sequence in context: A005897 A111694 A129111 this_sequence A163121 A002901 A050471
Adjacent sequences: A002410 A002411 A002412 this_sequence A002414 A002415 A002416
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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 James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999
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