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A093033
Number of interior balls in a truncated octahedral arrangement.
1
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.
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 08 2004
STATUS
approved