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 A005905 Number of points on surface of truncated tetrahedron: 14n^2 + 2 for n>0, a(0)=1. (Formerly M5001) 2

%I M5001

%S 1,16,58,128,226,352,506,688,898,1136,1402,1696,2018,2368,2746,3152,

%T 3586,4048,4538,5056,5602,6176,6778,7408,8066,8752,9466,10208,10978,

%U 11776,12602,13456,14338,15248,16186,17152,18146,19168,20218,21296,22402,23536,24698

%N Number of points on surface of truncated tetrahedron: 14n^2 + 2 for n>0, a(0)=1.

%C Also sequence found by reading the segment (1, 16) together with the line from 16, in the direction 16, 58,..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. - _Omar E. Pol_, Nov 05 2012

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

%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="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 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.

%p A005905:=-(z+1)*(z**2+12*z+1)/(z-1)**3; # [_Simon Plouffe_ in his 1992 dissertation.]

%t a[0] = 1; a[n_] := 14 n^2 + 2; Table[a[n], {n, 0, 50}] (* _Wesley Ivan Hurt_, Mar 04 2014 *)

%o (PARI) a(n) = if (n==0, 1, 14*n^2+2); \\ _Michel Marcus_, Mar 04 2014

%Y Cf. A206399.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Michel Marcus_, Mar 04 2014

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Last modified January 16 19:43 EST 2019. Contains 319206 sequences. (Running on oeis4.)