This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A052899 G.f.: ( 1-2*x ) / ((x-1)*(4*x^2+2*x-1)). 4
 1, 1, 5, 13, 45, 141, 461, 1485, 4813, 15565, 50381, 163021, 527565, 1707213, 5524685, 17878221, 57855181, 187223245, 605867213, 1960627405, 6344723661, 20531956941, 66442808525, 215013444813, 695798123725, 2251650026701 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Contribution by L. Edson Jeffery, Apr 19 2011. (Start): Let A be the unit-primitive matrix (see [Jeffery]) A=A_(10,4)= (0 0 0 0 1) (0 0 0 2 0) (0 0 2 0 1) (0 2 0 2 0) (2 0 2 0 1). Then a(n)=(1/5)*Trace(A^n). (End) LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 875 L. E. Jeffery, Unit-primitive matrices Index entries for linear recurrences with constant coefficients, signature (3,2,-4). FORMULA Recurrence: {a(1)=1, a(0)=1, -4*a(n)-2*a(n+1)+a(n+2)+1 =0} Sum(-1/25*(-1-8*_alpha+4*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z-2*_Z^2+4*_Z^3)) a(n)/a(n-1) tends to (1 + sqrt(5)) = 3.236067... - Gary W. Adamson, Mar 01 2008 a(n)=(1/5)*Sum_{k=1..5} ((x_k)^4-3*(x_k)^2+1), x_k=2*cos((2*k-1)*Pi/10). Also, a(n)/a(n-1) -> spectral radius of matrix A_(10,4) above. - L. Edson Jeffery, Apr 19 2011 a(n) = (2*A087131(n)+1)/5. - Bruno Berselli, Apr 20 2011 MAPLE spec := [S, {S=Sequence(Prod(Union(Sequence(Union(Z, Z)), Z, Z), Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20); MATHEMATICA CoefficientList[Series[(1-2x)/((x-1)(4x^2+2x-1)), {x, 0, 40}], x] (* or *) LinearRecurrence[{3, 2, -4}, {1, 1, 5}, 40] (* Harvey P. Dale, Jul 10 2017 *) PROG (Sage) from sage.combinat.sloane_functions import recur_gen2b it = recur_gen2b(1, 1, 2, 4, lambda n:-1) [it.next() for i in xrange(1, 28)] - Zerinvary Lajos, Jul 09 2008 (MAGMA) [(1/5)*(2^(n+1)*Lucas(n)+1): n in [0..50]]; // Vincenzo Librandi, Apr 20 2011 (Maxima)  makelist(coeff(taylor((1-2*x)/(1-3*x-2*x^2+4*x^3), x, 0, n), x, n), n, 0, 25); [Bruno Berselli, May 30 2011] CROSSREFS Cf. A084057. Sequence in context: A218926 A113835 A006349 * A147200 A147396 A099972 Adjacent sequences:  A052896 A052897 A052898 * A052900 A052901 A052902 KEYWORD easy,nonn AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 EXTENSIONS More terms from James A. Sellers, Jun 08 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.