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 A004467 a(n) = n*(11*n^2 - 5)/6. 17
 0, 1, 13, 47, 114, 225, 391, 623, 932, 1329, 1825, 2431, 3158, 4017, 5019, 6175, 7496, 8993, 10677, 12559, 14650, 16961, 19503, 22287, 25324, 28625, 32201, 36063, 40222, 44689, 49475, 54591, 60048 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 3-dimensional analog of centered polygonal numbers, that is: centered hendecagonal pyramidal numbers (see Deza paper in References). REFERENCES E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 140. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..5000 T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11). Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1). FORMULA G.f.: x*(1+9*x+x^2)/(1-x)^4. - Colin Barker, Jan 08 2012 a(0)=0, a(1)=1, a(2)=13, a(3)=47; for n>3, a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Sep 22 2013 E.g.f.: (x/6)*(6 + 33*x + 11*x^2)*exp(x). - G. C. Greubel, Sep 01 2017 MATHEMATICA Table[n(11n^2-5)/6, {n, 0, 80}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *) LinearRecurrence[{4, -6, 4, -1}, {0, 1, 13, 47}, 80] (* Harvey P. Dale, Sep 22 2013 *) PROG (MAGMA) [n*(11*n^2-5)/6: n in [0..50]]; // Vincenzo Librandi, May 15 2011 (PARI) a(n)=n*(11*n^2-5)/6 \\ Charles R Greathouse IV, Sep 28 2011 CROSSREFS 1/12*t*(n^3-n)+n for t = 2, 4, 6, ... gives A004006, A006527, A006003, A005900, A004068, A000578, A004126, A000447, A004188, A004466, A004467, A007588, A062025, A063521, A063522, A063523. Sequence in context: A031390 A113943 A222962 * A261395 A141865 A233059 Adjacent sequences:  A004464 A004465 A004466 * A004468 A004469 A004470 KEYWORD nonn,easy AUTHOR Albert D. Rich (Albert_Rich(AT)msn.com). STATUS approved

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Last modified October 20 16:08 EDT 2019. Contains 328268 sequences. (Running on oeis4.)