A005911 Number of points on surface of truncated cube: 46n^2 + 2 for n>0. (Formerly M5292)

1, 48, 186, 416, 738, 1152, 1658, 2256, 2946, 3728, 4602, 5568, 6626, 7776, 9018, 10352, 11778, 13296, 14906, 16608, 18402, 20288, 22266, 24336, 26498, 28752, 31098, 33536, 36066, 38688, 41402, 44208, 47106, 50096, 53178, 56352, 59618, 62976, 66426, 69968

Offset

0,2

References

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

B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Links

Table of n, a(n) for n=0..39.

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

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Formula

G.f.: 1 -2*x*(24+21*x+x^2)/(x-1)^3. - Simon Plouffe in his 1992 dissertation

a(0)=1, a(1)=48, a(2)=186, a(3)=416, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Aug 19 2014

Sum_{n>=0} 1/a(n) = 3/4+ 1/92 *sqrt(23)*Pi*coth(Pi/sqrt 23) = 1.03477653.... - R. J. Mathar, May 07 2024

Mathematica

Join[{1}, Table[46n^2+2, {n, 50}]] (* or *) Join[{1}, LinearRecurrence[{3, -3, 1}, {48, 186, 416}, 50]] (* Harvey P. Dale, Aug 19 2014 *)

Prog

(PARI) a(n)=if(n, 46*n^2+2, 1) \\ Charles R Greathouse IV, Oct 20 2022

Crossrefs

Sequence in context: A066134 A233682 A233675 * A130566 A233792 A233967

Adjacent sequences: A005908 A005909 A005910 * A005912 A005913 A005914

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Harvey P. Dale, Aug 19 2014

Status

approved