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%I M4607 #31 Dec 27 2021 21:46:12
%S 1,9,30,65,114,177,254,345,450,569,702,849,1010,1185,1374,1577,1794,
%T 2025,2270,2529,2802,3089,3390,3705,4034,4377,4734,5105,5490,5889,
%U 6302,6729,7170,7625,8094,8577,9074,9585,10110,10649,11202,11769,12350,12945,13554
%N Number of points on surface of tricapped prism: 7n^2 + 2 for n > 0, a(0)=1.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%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://dx.doi.org/10.1021/ic00220a025">Magic numbers in polygonal and polyhedral clusters</a>, Inorgan. Chem. 24 (1985), 4545-4558.
%p A005919:=-(z+1)*(z**2+5*z+1)/(z-1)**3; # conjectured by _Simon Plouffe_ in his 1992 dissertation
%t Join[{1},7*Range[50]^2+2] (* or *) CoefficientList[Series[(-x^3-6x^2-6x-1)/(x-1)^3,{x,0,50}],x] (* _Harvey P. Dale_, Jan 13 2013 *)
%Y Cf. A206399.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Erich Friedman_, Aug 08 2005
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