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A004466 a(n) = n*(5*n^2 - 2)/3. 22
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
T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11).
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
Cf. A062786 (first differences), A264853 (partial sums).
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
KEYWORD
nonn,easy
AUTHOR
Albert D. Rich (Albert_Rich(AT)msn.com)
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)