A005903 Number of points on surface of dodecahedron: 30n^2 + 2 for n > 0.

1, 32, 122, 272, 482, 752, 1082, 1472, 1922, 2432, 3002, 3632, 4322, 5072, 5882, 6752, 7682, 8672, 9722, 10832, 12002, 13232, 14522, 15872, 17282, 18752, 20282, 21872, 23522, 25232, 27002, 28832, 30722, 32672, 34682, 36752, 38882, 41072, 43322, 45632, 48002

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• H. S. M. Coxeter, Polyhedral Numbers, in R. S. Cohen et al., editors, For Dirk Struik. Reidel, Dordrecht, 1974, pp. 25-35.
• 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).

Crossrefs

Cf. A206399.

Programs

Maple

A005903:=-(z+1)*(z**2+28*z+1)/(z-1)**3; [Simon Plouffe in his 1992 dissertation.]

Mathematica

Join[{1}, 30 Range[40]^2 + 2] (* Bruno Berselli, Feb 07 2012 *)

PARI

a(n) = if (n==0, 1, 30*n^2+2); \\ Michel Marcus, Mar 04 2014

Formula

G.f.: (1+x)*(1+28*x+x^2)/(1-x)^3. - Simon Plouffe (see MAPLE line)

Sum_{n>=0} 1/a(n) = 3/4 + Pi*sqrt(15)*coth(Pi/sqrt 15)/60 = 1.052567... - R. J. Mathar, Apr 27 2024