A296954 Expansion of x*(1 - x + 4*x^2) / ((1 - x)*(1 - 2*x)).
0, 1, 2, 8, 20, 44, 92, 188, 380, 764, 1532, 3068, 6140, 12284, 24572, 49148, 98300, 196604, 393212, 786428, 1572860, 3145724, 6291452, 12582908, 25165820, 50331644, 100663292, 201326588, 402653180, 805306364, 1610612732, 3221225468, 6442450940, 12884901884
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- J. Devillet, Bisymmetric and quasitrivial operations: characterizations and enumerations, arXiv:1712.07856 [math.RA] (2017).
- Index entries for linear recurrences with constant coefficients, signature (3,-2).
Crossrefs
Cf. A296953.
Programs
-
Mathematica
CoefficientList[Series[x (1 - x + 4 x^2)/((1 - x) (1 - 2 x)), {x, 0, 33}], x] (* Michael De Vlieger, Dec 23 2017 *) LinearRecurrence[{3,-2},{0,1,2,8},40] (* Harvey P. Dale, Jun 05 2021 *) -
PARI
concat(0, Vec(x*(1 - x + 4*x^2) / ((1 - x)*(1 - 2*x)) + O(x^40))) \\ Colin Barker, Dec 22 2017
Formula
a(n) = A296953(n)-2, a(0)=0, a(1)=1.
From Colin Barker, Dec 22 2017: (Start)
G.f.: x*(1 - x + 4*x^2) / ((1 - x)*(1 - 2*x)).
a(n) = 3*2^(n-1) - 4 for n>1.
a(n) = 3*a(n-1) - 2*a(n-2) for n>3.
(End)
Extensions
G.f. in the name replaced by a better g.f. by Colin Barker, Dec 23 2017
Comments