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

1, 16, 58, 128, 226, 352, 506, 688, 898, 1136, 1402, 1696, 2018, 2368, 2746, 3152, 3586, 4048, 4538, 5056, 5602, 6176, 6778, 7408, 8066, 8752, 9466, 10208, 10978, 11776, 12602, 13456, 14338, 15248, 16186, 17152, 18146, 19168, 20218, 21296, 22402, 23536, 24698

Offset

0,2

Comments

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

References

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

Links

Table of n, a(n) for n=0..42.

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.

Maple

A005905:=-(z+1)*(z**2+12*z+1)/(z-1)**3; # [Simon Plouffe in his 1992 dissertation.]

Mathematica

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

Prog

(PARI) a(n) = if (n==0, 1, 14*n^2+2); \\ Michel Marcus, Mar 04 2014

Crossrefs

Cf. A206399.

Sequence in context: A235736 A235517 A253428 * A177890 A225922 A235510

Adjacent sequences: A005902 A005903 A005904 * A005906 A005907 A005908

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Michel Marcus, Mar 04 2014

Status

approved