A107383 a(n) = 2*a(n-2) + 2*a(n-3).

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

Offset: 0

Author

Roger L. Bagula, May 24 2005

Keywords

• nonn
• easy

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

• Michael De Vlieger, Table of n, a(n) for n = 0..4037
• Igor Pak, Boris Shapiro, Ilya Smirnov, and Ken-ichi Yoshida, Hilbert-Kunz multiplicity of quadrics via the Ehrhart theory, Stockholm Univ. (Sweden, 2025). See p. 4.
• Noriaki Sannomiya, Hosho Katsura, and Yu Nakayama, Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion, arXiv:1612.02285 [cond-mat.str-el], 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).

Crossrefs

Cf. A061279, A078025.

Programs

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}] (* edited and corrected by Harvey P. Dale, May 07 2014 *)
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 *)

Formula

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

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

Limit_{n->oo} a(n)/a(n-1) = 1.7692923... .

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

Extensions

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