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Search: id:A052899
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| A052899 |
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G.f.: (1-2*x)/(1-3*x-2*x^2+4*x^3) |
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+0
2
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| 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; listen)
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OFFSET
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0,3
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COMMENT
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A simple regular expression.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 875
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FORMULA
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Recurrence: {a(1)=1, a(0)=1, -4*a(n)-2*a(n+1)+a(n+2)+1}
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 (qntmpkt(AT)yahoo.com), Mar 01 2008
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MAPLE
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spec := [S, {S=Sequence(Prod(Union(Sequence(Union(Z, Z)), Z, Z), Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROGRAM
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sage: from sage.combinat.sloane_functions import recur_gen2b sage: it = recur_gen2b(1, 1, 2, 4, lambda n:-1) sage: [it.next() for i in xrange(1, 28)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 09 2008
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CROSSREFS
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Sequence in context: A115785 A113835 A006349 this_sequence A147200 A147396 A099972
Adjacent sequences: A052896 A052897 A052898 this_sequence A052900 A052901 A052902
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 08 2000
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