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 A006007 4-dimensional analog of centered polygonal numbers: a(n) = n(n+1)*(n^2+n+4)/12. (Formerly M3865) 14
 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; text; internal format)
 OFFSET 0,3 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, Towards Classifying Finite Point-Set Configurations, preprint, 1997. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..710 S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy) Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1). 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). - Harvey P. Dale, Sep 30 2011 For n>0, a(n) = (A000217(n-1)^2 + A000217(n)^2 + A000217(n+1)^2 - 1)/9. - Richard R. Forberg, Dec 25 2013 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 (* Vladimir Joseph Stephan Orlovsky, 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] (* Harvey P. Dale, Sep 30 2011 *) PROG (MAGMA) [n*(n+1)*(n^2+n+4)/12: n in [0..60]]; // Vincenzo Librandi, Apr 26 2011 (PARI) a(n)=n*(n+1)*(n^2+n+4)/12 \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A003215, A000537, A000578, A005898, A027602. - Vladimir Joseph Stephan Orlovsky, Jan 03 2009 Sequence in context: A011863 A027085 A099452 * A001753 A202087 A309403 Adjacent sequences:  A006004 A006005 A006006 * A006008 A006009 A006010 KEYWORD easy,nonn,nice AUTHOR EXTENSIONS More terms from Henry Bottomley, Apr 24 2001 STATUS approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)