A005903 Number of points on surface of dodecahedron: 30n^2 + 2 for n > 0. (Formerly M5230)

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

0,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A206399.

Sequence in context: A223314 A203965 A203958 * A344219 A271532 A264480

Adjacent sequences: A005900 A005901 A005902 * A005904 A005905 A005906

Keyword

nonn,easy,changed

Author

N. J. A. Sloane.

Status

approved