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 A004188 a(n) = n*(3*n^2 - 1)/2. 24
 0, 1, 11, 39, 94, 185, 321, 511, 764, 1089, 1495, 1991, 2586, 3289, 4109, 5055, 6136, 7361, 8739, 10279, 11990, 13881, 15961, 18239, 20724, 23425, 26351, 29511, 32914, 36569, 40485, 44671, 49136, 53889, 58939, 64295, 69966, 75961 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 3-dimensional analog of centered polygonal numbers. (1), (4+7), (10+13+16), (19+22+25+28), ... - Jon Perry, Sep 10 2004 REFERENCES E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 140. T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..5000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA Partial sums of n-1 3-spaced triangular numbers, e.g., a(4) = t(1) + t(4) + t(7) = 1 + 10 + 28 = 39. - Jon Perry, Jul 23 2003 a(n) = C(2*n+1,3) + C(n+1,3), n >= 0. - Zerinvary Lajos, Jan 21 2007 a(n) = A000447(n) + A000292(n). - Zerinvary Lajos, Jan 21 2007 G.f.: x*(1+7*x+x^2) / (x-1)^4. - R. J. Mathar, Oct 08 2011 From Miquel Cerda, Dec 25 2016: (Start) a(n) = A000578(n) + A135503(n). a(n) = A007588(n) - A135503(n). (End) E.g.f.: (x/2)*(2 + 9*x + 3*x^2)*exp(x). - G. C. Greubel, Sep 01 2017 MAPLE seq(binomial(2*n+1, 3)+binomial(n+1, 3), n=0..37); # Zerinvary Lajos, Jan 21 2007 MATHEMATICA Table[n(3n^2-1)/2, {n, 0, 80}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *) LinearRecurrence[{4, -6, 4, -1}, {0, 1, 11, 39}, 40] (* Harvey P. Dale, Jul 19 2019 *) PROG (PARI) vector(40, n, n*(3*n^2-1)/2) (MAGMA) [n*(3*n^2-1)/2: n in [0..50]]; //Vincenzo Librandi, May 15 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. Cf. A002412, A016061, A051682. Cf. A236770 (partial sums). Sequence in context: A103738 A045801 A162261 * A163634 A173373 A127867 Adjacent sequences:  A004185 A004186 A004187 * A004189 A004190 A004191 KEYWORD nonn,easy AUTHOR Albert D. Rich (Albert_Rich(AT)msn.com) STATUS approved

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Last modified August 24 16:16 EDT 2019. Contains 326295 sequences. (Running on oeis4.)