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A006007
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4-dimensional analogue of centered polygonal numbers: a(n) = n(n+1)*(n^2+n+4)/12.
(Formerly M3865)
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11
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0, 1, 5, 16, 40, 85, 161, 280, 456, 705, 1045, 1496, 2080, 2821, 3745, 4880, 6256, 7905, 9861, 12160, 14840, 17941, 21505, 25576, 30200, 35425, 41301, 47880, 55216, 63365, 72385, 82336, 93280, 105281, 118405, 132720, 148296, 165205, 183521
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D.-N. Verma (dnverma(AT)math.tifr.res.in), Towards Classifying Finite Point-Set Configurations, preprint, 1997.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..710
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FORMULA
| G.f.: (1+x^2)/(1-x)^5.
a(n) = 2*binomial(n + 2, 4) + binomial(n + 1, 2).
a(n) = A061316(n)/3 = A061315(n, 3) = sqrt(A061318(n)-A061316(n)).
a(0)=0, a(1)=1, a(2)=5, a(3)=16, a(4)=40, a(n)=5*a(n-1)- 10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) [From Harvey P. Dale, Sep 30 2011]
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MATHEMATICA
| f[n_]:=n^3; lst={}; s=0; Do[s+=(f[n]+f[n+1]+f[n+2]); AppendTo[lst, s/9], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 03 2009]
Table[2Binomial[n+2, 4]+Binomial[n+1, 2], {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 5, 16, 40}, 40] (* From Harvey P. Dale, Sep 30 2011 *)
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PROG
| (MAGMA) [n*(n+1)*(n^2+n+4)/12: n in [0..60]]; // Vincenzo Librandi, Apr 26 2011
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CROSSREFS
| Cf. A003215, A000537, A000578, A005898, A027602 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 03 2009]
Sequence in context: A011863 A027085 A099452 * A001753 A202087 A073459
Adjacent sequences: A006004 A006005 A006006 * A006008 A006009 A006010
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KEYWORD
| easy,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| More terms from Henry Bottomley (se16(AT)btinternet.com), Apr 24 2001
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