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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 (list; graph; refs; listen; history; text; internal format)
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 3-D 4-connected nets ..., J. Solid State Chem 27 1979 349-355, 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)) / ((1-x)^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 b-file. 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}] (* Jean-Fran├žois 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

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Last modified December 5 05:12 EST 2016. Contains 278760 sequences.