A005903 - OEIS

%I M5230 #42 Apr 27 2024 15:03:23

%S 1,32,122,272,482,752,1082,1472,1922,2432,3002,3632,4322,5072,5882,

%T 6752,7682,8672,9722,10832,12002,13232,14522,15872,17282,18752,20282,

%U 21872,23522,25232,27002,28832,30722,32672,34682,36752,38882,41072,43322,45632,48002

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

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

%H Bruno Berselli, <a href="/A005903/b005903.txt">Table of n, a(n) for n = 0..1000</a>

%H H. S. M. Coxeter, <a href="http://dx.doi.org/10.1007/978-94-010-2115-9_4">Polyhedral Numbers</a>, in R. S. Cohen et al., editors, For Dirk Struik. Reidel, Dordrecht, 1974, pp. 25-35.

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H B. K. Teo and N. J. A. Sloane, <a href="http://neilsloane.com/doc/magic1/magic1.html">Magic numbers in polygonal and polyhedral clusters</a>, Inorgan. Chem. 24 (1985),4545-4558.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: (1+x)*(1+28*x+x^2)/(1-x)^3. - _Simon Plouffe_ (see MAPLE line)

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

%p A005903:=-(z+1)*(z**2+28*z+1)/(z-1)**3; [_Simon Plouffe_ in his 1992 dissertation.]

%t Join[{1}, 30 Range[40]^2 + 2] (* _Bruno Berselli_, Feb 07 2012 *)

%o (PARI) a(n) = if (n==0, 1, 30*n^2+2); \\ _Michel Marcus_, Mar 04 2014

%Y Cf. A206399.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.