

A008577


Crystal ball sequence for planar net 4.8.8.


4



1, 4, 9, 17, 28, 41, 57, 76, 97, 121, 148, 177, 209, 244, 281, 321, 364, 409, 457, 508, 561, 617, 676, 737, 801, 868, 937, 1009, 1084, 1161, 1241, 1324, 1409, 1497, 1588, 1681, 1777, 1876, 1977, 2081
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OFFSET

0,2


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000
W. M. Meier and H. J. Moeck, Topology of 3D 4connected nets ..., J. Solid State Chem 27 1979 349355, esp. p. 351.
Index entries for crystal ball sequences
Index entries for linear recurrences with constant coefficients, signature (2,1,1,2,1).


FORMULA

G.f.: ((1+x)^2*(1+x^2)) / ((1x)^3*(1+x+x^2)).  Ralf Stephan, Apr 24 2004
a(n) = 4*(n/3)*(n+1)+10/9+A099837(n+2)/9.  R. J. Mathar, Nov 20 2010
The above g.f. and formula were originally stated as conjectures, but I now have a proof. This also justifies the bfile. Details will be added later.  N. J. A. Sloane, Dec 29 2015


MATHEMATICA

A099837[0] = 1; A099837[n_] := Mod[n+2, 3]  Mod[n, 3]; a[n_] := 4*n/3*(n+1) + 10/9 + A099837[n+2]/9; Table[a[n], {n, 0, 39}] (* JeanFrançois Alcover, Feb 15 2012, after R. J. Mathar *)
CoefficientList[Series[((1 + x)^2 (1 + x^2))/((1  x)^3 (1 + x + x^2)), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 31 2015 *)


CROSSREFS

Partial sums of A008576.
Cf. A099837.
Sequence in context: A033617 A033613 A033608 * A033605 A008137 A008023
Adjacent sequences: A008574 A008575 A008576 * A008578 A008579 A008580


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane


STATUS

approved



