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A107383 a(n) = 2*a(n-2) + 2*a(n-3). 2
0, 1, 1, 2, 4, 6, 12, 20, 36, 64, 112, 200, 352, 624, 1104, 1952, 3456, 6112, 10816, 19136, 33856, 59904, 105984, 187520, 331776, 587008, 1038592, 1837568, 3251200, 5752320, 10177536, 18007040, 31859712, 56369152, 99733504, 176457728 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Also the number of maximal independent vertex sets (and minimal vertex covers) in the 2 X (n-2) king graph. - Eric W. Weisstein, Aug 07 2017

LINKS

Table of n, a(n) for n=0..35.

Noriaki Sannomiya, H Katsura, Y Nakayama, Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion, arXiv preprint arXiv:1612.02285, 2016. See Table II, line 1.

Eric Weisstein's World of Mathematics, King Graph

Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set

Eric Weisstein's World of Mathematics, Minimal Vertex Cover

Index entries for linear recurrences with constant coefficients, signature (0,2,2).

FORMULA

G.f.: x*(1+x)/(1-2*x^2-2*x^3).

a(n) = (-1)^(n+1)*A078025(n-1).

Limit a(n)/a(n-1) = 1.7692923... .

a(n)+a(n+1) = A061279(n). - R. J. Mathar, Dec 01 2011

MATHEMATICA

m = 2; a[0] = 0; a[1] = 1; a[2] = 1; a[3] = 2; a[n_] := a[n] = a[n - 1] + m*a[n - 2] - m*a[n - 4]; Table[a[n], {n, 0, 50}]

LinearRecurrence[{0, 2, 2}, {0, 1, 1}, 40] (* Harvey P. Dale, May 07 2014 *)

Table[RootSum[-2 - 2 # + #^3 &, 5 #^n + 8 #^(n + 1) + #^(n + 2) &]/19, {n, 20}] (* Eric W. Weisstein, Aug 07 2017 *)

CoefficientList[Series[-((2 (1 + 2 x + x^2))/(-1 + 2 x^2 + 2 x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 07 2017 *)

CROSSREFS

Sequence in context: A329227 A294430 A294429 * A078025 A178901 A164146

Adjacent sequences:  A107380 A107381 A107382 * A107384 A107385 A107386

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, May 24 2005

EXTENSIONS

Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009

First Mathematica program edited and corrected by Harvey P. Dale, May 07 2014

STATUS

approved

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Last modified September 22 13:41 EDT 2021. Contains 347607 sequences. (Running on oeis4.)