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Search: id:A052542
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| A052542 |
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a(0) = 1, a(1) = 2, a(2) = 4; for n>=3, a(n) = 2a(n-1) + a(n-2). |
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13
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| 1, 2, 4, 10, 24, 58, 140, 338, 816, 1970, 4756, 11482, 27720, 66922, 161564, 390050, 941664, 2273378, 5488420, 13250218, 31988856, 77227930, 186444716, 450117362, 1086679440, 2623476242, 6333631924, 15290740090, 36915112104, 89120964298
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Apart from the initial 1, this sequence is simply twice the Pell numbers, A000129. - Antonio Alberto Olivares (tonioolivares(AT)todito.com), Dec 31 2003
Image of 1/(1-2x) under the mapping g(x)->g(x/(1+x^2)). - Paul Barry (pbarry(AT)wit.ie), Jan 16 2005
The intermediate convergents to 2^(1/2) begin with 4/3, 10/7, 24/17, 58/41; essentially, numerators=A052542 and denominators=A001333. - Clark Kimberling (ck6(AT)evansville.edu), Aug 26 2008
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 477
C. Banderier and D. Merlini, Lattice paths with an infinite set of jumps, FPSAC02, Melbourne, 2002.
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FORMULA
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G.f.: (-1+x^2)/(-1+2*x+x^2)
Recurrence: {a(0)=1, a(2)=4, a(1)=2, a(n)+2*a(n+1)-a(n+2)}
Sum(-1/2*(-1+_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+_Z^2))
a(n)=2*A001333(n-1)+a(n-1), n>1. A001333(n)/a(n) converges to sqrt(1/2). - Mario Catalani (mario.catalani(AT)unito.it), Apr 29 2003
Binomial transform of A094024. a(n)=0^n+((1+sqrt(2))^n-(1-sqrt(2))^n)/sqrt(2). - Paul Barry (pbarry(AT)wit.ie), Apr 22 2004
a(n)=sum{k=0..floor(n/2), binomial(n-k-1, k)2^(n-2k)} - Paul Barry (pbarry(AT)wit.ie), Jan 16 2005
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MAPLE
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spec := [S, {S=Sequence(Prod(Union(Z, Z), Sequence(Prod(Z, Z))))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
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Cf. A052906.
Sequence in context: A025275 A165409 A163271 this_sequence A110236 A065161 A038373
Adjacent sequences: A052539 A052540 A052541 this_sequence A052543 A052544 A052545
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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 05 2000
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