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A160250 64*n^3-168*n^2+148*n-43. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Rhombic-dodecahedron figurate quantities, in face-centered-cubic sphere packing, and with every vertex terminating in a single unit.

These have non-contiguous 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 2n-1 ribs on each face. The long diagonal has 4n-3 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) / (x-1)^4 . - R. J. Mathar, Nov 10 2011

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jul 01 2012

MATHEMATICA

CoefficientList[Series[(1+89*x+251*x^2+43*x^3)/(x-1)^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()^3-168*ROW()^2+148*ROW()-43

(MAGMA) I:=[1, 93, 617, 1957]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jul 01 2012

(PARI) a(n)=64*n^3-168*n^2+148*n-43 \\ 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. Spies-Rusk (chaosorder4(AT)gmail.com), May 05 2009, May 11 2009, May 19 2009

STATUS

approved

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Last modified April 23 13:25 EDT 2019. Contains 322386 sequences. (Running on oeis4.)