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A052995
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Expansion of 2x(1-x)/(1-3x+x^2).
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5
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0, 2, 4, 10, 26, 68, 178, 466, 1220, 3194, 8362, 21892, 57314, 150050, 392836, 1028458, 2692538, 7049156, 18454930, 48315634, 126491972, 331160282, 866988874, 2269806340, 5942430146, 15557484098, 40730022148, 106632582346
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OFFSET
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0,2
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COMMENTS
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Terms >=4 give solutions x to floor(phi^2*x^2)-floor(phi*x)^2 = 5, where phi=(1+sqrt(5))/2 - Benoit Cloitre, Mar 16 2003
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 30.
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LINKS
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Table of n, a(n) for n=0..27.
Guo-Niu Han, Enumeration of Standard Puzzles
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1072
Index to sequences with linear recurrences with constant coefficients, signature (3,-1).
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FORMULA
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G.f.: -2*x*(-1+x)/(1-3*x+x^2)
Recurrence: {a(0)=0, a(2)=4, a(1)=2, a(n)-3*a(n+1)+a(n+2)=0}
Sum(2/5*(-1+4*_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^2-3*_Z+1))
a(n) = 2*Fibonacci(2*n-1), n>0. - Vladeta Jovovic, Mar 19 2003
a(n+2) = F(n)^2 + F(n+3)^2 = 2F(n+1)^2 + 2F(n+2)^2.
a(n)=1/2*(fib(2n+8) mod fib(2n+2)), n>2
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MAPLE
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spec := [S, {S=Prod(Sequence(Union(Prod(Sequence(Z), Z), Z)), Union(Z, Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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CROSSREFS
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Equals A069403(n-1)+1. Bisection of A006355. First differences of A025169. Cf. A055819.
Sequence in context: A095337 A162533 * A055819 A113337 A084575 A081881
Adjacent sequences: A052992 A052993 A052994 * A052996 A052997 A052998
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KEYWORD
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easy,nonn,changed
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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, Jun 05 2000
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STATUS
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approved
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