OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).
FORMULA
a(n) = (3*n+1)^3 - 8*(n)*(n+1)*(n+2)/6 = (77/3)*n^3 + 23*n^2 + (19/3)*n + 1.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=56, a(2)=311, a(3)=920. - Harvey P. Dale, Aug 14 2011
MAPLE
A005912:=(1+52*z+93*z**2+8*z**3)/(z-1)**4; # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
Table[(3n+1)^3-8(n)(n+1)(n+2)/6, {n, 0, 30}] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {1, 56, 311, 920}, 30] (* Harvey P. Dale, Aug 14 2011 *)
PROG
(Haskell)
a005912 n = (n * (n * (77 * n + 69) + 19) + 3) `div` 3 :: Integer
-- Reinhard Zumkeller, Aug 09 2014
(Magma) [(3*n+1)^3-8*(n)*(n+1)*(n+2)/6: n in [0..40]] // Vincenzo Librandi, Aug 09 2014
(PARI) a(n)=(3*n+1)^3-8*(n)*(n+1)*(n+2)/6 \\ Charles R Greathouse IV, Feb 10 2017
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 22 1999
STATUS
approved