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A004466 a(n) = n*(5*n^2 - 2)/3. 20
0, 1, 12, 43, 104, 205, 356, 567, 848, 1209, 1660, 2211, 2872, 3653, 4564, 5615, 6816, 8177, 9708, 11419, 13320, 15421, 17732, 20263, 23024, 26025, 29276, 32787, 36568, 40629, 44980, 49631, 54592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

3-dimensional analog of centered polygonal numbers.

Also as a(n)=(1/6)*(10*n^3-4*n), n>0: structured pentagonal anti-diamond numbers (vertex structure 11) (Cf. A051673 = alternate vertex A100188 = structured anti-diamonds; A100145 for more on structured numbers). - James A. Record (james.record(AT)gmail.com), Nov 07 2004

a(n+1)-10*a(n) = (n+1)*(5*(n+1)^2-2)/3 - (10n(n+1)(n+2)/6) = n. The unit digits are 0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,... . - Eric Desbiaux, Aug 18 2008

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+8*x+x^2)/(1-x)^4. - Colin Barker, Jan 08 2012

E.g.f.: (x/3)*(3 + 15*x + 5*x^2)*exp(x). - G. C. Greubel, Sep 01 2017

MAPLE

A004466:=n->n*(5*n^2 - 2)/3; seq(A004466(n), n=0..50); # Wesley Ivan Hurt, Mar 10 2014

MATHEMATICA

Table[n(5n^2-2)/3, {n, 0, 80}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)

PROG

(MAGMA) [n*(5*n^2-2)/3: n in [0..50]]; // Vincenzo Librandi, May 15 2011

(PARI) a(n)=n*(5*n^2-2)/3 \\ Charles R Greathouse IV, Sep 24 2015

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: A253911 A082829 A003357 * A062749 A251929 A004636

Adjacent sequences:  A004463 A004464 A004465 * A004467 A004468 A004469

KEYWORD

nonn,easy

AUTHOR

Albert D. Rich (Albert_Rich(AT)msn.com)

STATUS

approved

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Last modified February 19 13:25 EST 2018. Contains 299333 sequences. (Running on oeis4.)