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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 February 21 12:54 EST 2018. Contains 299411 sequences. (Running on oeis4.)