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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
T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11).
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
KEYWORD
nonn,easy
AUTHOR
Albert D. Rich (Albert_Rich(AT)msn.com).
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)