OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
L. Hogben, Choice and Chance by Cardpack and Chessboard, Vol. 1, Max Parrish and Co, London, 1950, p. 36.
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 (3,-3,1).
FORMULA
a(n) = a(n-1) + 14*n - 3 (with a(0)=1). - Vincenzo Librandi, Nov 18 2010
From G. C. Greubel, Nov 30 2017: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: (1 + 9*x + 4*x^2)/(1 - x)^3.
E.g.f.: (1 + 11*x + 7*x^2)*exp(x). (End)
MAPLE
A005892:=-(1+9*z+4*z**2)/(z-1)**3; # Simon Plouffe in his 1992 dissertation
MATHEMATICA
Table[7n^2+4n+1, {n, 0, 50}] (* Harvey P. Dale, Mar 24 2011 *)
PROG
(PARI) a(n)=7*n^2+4*n+1 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [7*n^2 + 4*n + 1: n in [0..50]]; // G. C. Greubel, Nov 30 2017
(Sage) [7*n^2+4*n+1 for n in (0..50)] # G. C. Greubel, Apr 19 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Frank Ellermann, Jan 18 2002
STATUS
approved