

A160250


64*n^3168*n^2+148*n43.


2



1, 93, 617, 1957, 4497, 8621, 14713, 23157, 34337, 48637, 66441, 88133, 114097, 144717, 180377, 221461, 268353, 321437, 381097, 447717, 521681, 603373, 693177, 791477, 898657, 1015101, 1141193
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OFFSET

1,2


COMMENTS

Rhombicdodecahedron figurate quantities, in facecenteredcubic sphere packing, and with every vertex terminating in a single unit.
These have noncontiguous edges and ribbed faces. A contiguous line is however formed by the long diagonal of each face, as well as ribs parallel to it.
Including the long diagonal, there are 2n1 ribs on each face. The long diagonal has 4n3 units for quantity. These volumes approach 4/3 of those of the octahedron / cube intersections (A160174).


REFERENCES

Main Title: Polyhedra primer / Peter Pearce and Susan Pearce. Published/Created: New York : Van Nostrand Reinhold, c1978. Description: viii, 134 p. : ill. ; 24 cm. ISBN: 0442264968
Main Title: The book of numbers / John H. Conway, Richard K. Guy. Published/Created: New York, NY : Copernicus c1996. Description: ix, 310 p. : ill. (some col.) ; 24 cm. ISBN: 038797993X


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,6,4,1).


FORMULA

G.f. x*(1+89*x+251*x^2+43*x^3) / (x1)^4 .  R. J. Mathar, Nov 10 2011
a(n) = 4*a(n1) 6*a(n2) +4*a(n3) a(n4).  Vincenzo Librandi, Jul 01 2012


MATHEMATICA

CoefficientList[Series[(1+89*x+251*x^2+43*x^3)/(x1)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 01 2012 *)
LinearRecurrence[{4, 6, 4, 1}, {1, 93, 617, 1957}, 30] (* Harvey P. Dale, Mar 16 2013 *)


PROG

(Excel) The following formula will give volumes corresponding to row numbers as n when filled down in a column:
=64*ROW()^3168*ROW()^2+148*ROW()43
(MAGMA) I:=[1, 93, 617, 1957]; [n le 4 select I[n] else 4*Self(n1)6*Self(n2)+4*Self(n3)Self(n4): n in [1..40]]; // Vincenzo Librandi, Jul 01 2012
(PARI) a(n)=64*n^3168*n^2+148*n43 \\ Charles R Greathouse IV, Apr 25 2016


CROSSREFS

Sequence in context: A146090 A160174 A238693 * A264556 A250373 A250374
Adjacent sequences: A160247 A160248 A160249 * A160251 A160252 A160253


KEYWORD

easy,nonn,uned


AUTHOR

Chris G. SpiesRusk (chaosorder4(AT)gmail.com), May 05 2009, May 11 2009, May 19 2009


STATUS

approved



