A093033 Number of interior balls in a truncated octahedral arrangement.

6, 79, 314, 807, 1654, 2951, 4794, 7279, 10502, 14559, 19546, 25559, 32694, 41047, 50714, 61791, 74374, 88559, 104442, 122119, 141686, 163239, 186874, 212687, 240774, 271231, 304154, 339639, 377782, 418679, 462426, 509119, 558854, 611727, 667834, 727271

Offset

1,1

References

H. S. M. Coxeter, Polyhedral numbers, pp. 25-35 of R. S. Cohen, J. J. Stachel and M. W. Wartofsky, eds., For Dirk Struik: Scientific, historical and political essays in honor of Dirk J. Struik, Reidel, Dordrecht, 1974.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 16*n^3 - 15*n^2 + 6*n - 1.

G.f.: x*(6 + 55*x + 34*x^2 + x^3)/(1-x)^4. - Colin Barker, Feb 12 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=6, a(2)=79, a(3)=314, a(4)=807. - Harvey P. Dale, Aug 11 2015

Mathematica

Table[16*n^3-15*n^2+6*n-1, {n, 1, 50}] (* Vincenzo Librandi, Feb 12 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {6, 79, 314, 807}, 50] (* Harvey P. Dale, Aug 11 2015 *)

Prog

(Magma) [16*n^3-15*n^2+6*n-1: n in [1..50]]; // Vincenzo Librandi, Feb 12 2012
(PARI) for(n=1, 40, print1(16*n^3-15*n^2+6*n-1", ")); \\ Vincenzo Librandi, Feb 12 2012

Crossrefs

Sequence in context: A353411 A053771 A294992 * A156929 A123796 A184553

Adjacent sequences: A093030 A093031 A093032 * A093034 A093035 A093036

Keyword

nonn,easy

Author

N. J. A. Sloane, May 08 2004

Status

approved