

A188128


Expansion of (46*x6*x^2+x^3)/((1+x)*(13*x+x^3)).


1



4, 2, 10, 23, 70, 197, 571, 1640, 4726, 13604, 39175, 112796, 324787, 935183, 2692756, 7753478, 22325254, 64283003, 185095534, 532961345, 1534601035, 4418707568, 12723161362, 36634883048, 105485941579, 303734663372, 874569107071
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OFFSET

0,1


COMMENTS

Let A_{9,3} = [0,0,0,1; 0,0,1,1; 0,1,1,1; 1,1,1,1], a unitprimitive matrix (see [Jeffery]). Then a(n) = Trace([A_{9,3}]^n).


LINKS

Table of n, a(n) for n=0..26.
L. E. Jeffery, Unitprimitive matrices
Index entries for linear recurrences with constant coefficients, signature (2, 3, 1, 1).


FORMULA

G.f.: (46*x6*x^2+x^3)/((1+x)*(13*x+x^3)).
a(n) = 2*a(n1)+3*a(n2)a(n3)a(n4), {a(m)}={4,2,10,23}, m=0,1,2,3.
a(n) = Sum_{k=1..4} ((x_k)^32*(x_k))^n, x_k=2*(1)^(k1)*cos(k*Pi/9).
a(n) = (1)^n+(1+2*cos(Pi/9))^n+(1cos(Pi/9)+sqrt(3)*sin(Pi/9))^n + (1cos(Pi/9)sqrt(3)*sin(Pi/9))^n.  L. Edson Jeffery, Dec 15 2011
a(n) = (1)^n + 3*A147704(n).  R. J. Mathar, Oct 08 2016


MATHEMATICA

CoefficientList[Series[(46x6x^2+x^3)/((1+x)(13x+x^3)), {x, 0, 30}], x] (* or *) LinearRecurrence[{2, 3, 1, 1}, {4, 2, 10, 23}, 30] (* Harvey P. Dale, Apr 22 2011 *)


CROSSREFS

Sequence in context: A128781 A135440 A215500 * A091484 A163544 A191728
Adjacent sequences: A188125 A188126 A188127 * A188129 A188130 A188131


KEYWORD

nonn,easy


AUTHOR

L. Edson Jeffery, Apr 05 2011


STATUS

approved



