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Search: id:A078343
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| A078343 |
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a(0) = -1, a(1) = 2; a(n) = 2*a(n-1) + a(n-2). |
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+0
7
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| -1, 2, 3, 8, 19, 46, 111, 268, 647, 1562, 3771, 9104, 21979, 53062, 128103, 309268, 746639, 1802546, 4351731, 10506008, 25363747, 61233502, 147830751, 356895004, 861620759, 2080136522, 5021893803, 12123924128, 29269742059, 70663408246, 170596558551
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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H. S. M. Coxeter, 1998, Numerical distances among the circles in a loxodromic sequence, Nieuw Arch. Wisk, 16, pp. 1-9.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
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For the unsigned version: a(1)=1; a(2)=2; a(n) = sum(k=2, n-1, a(k) + a(k-1) ).
a(n) is asymptotic to (1/4)*(8-5*sqrt(2))*(1+sqrt(2))^n.
a(n) = A048746(n-3) + 2, for n>2. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 17 2003
a(n)=2Pell(n)-Pell(n-1); abs(A078343(n))=2*0^n+2Pell(n)-Pell(n-1); abs(A078343(n))=sum{k=0..floor(n/2), (C(n-k-1, k)-C(n-k-1, k-1))2^(n-2k)} - Paul Barry (pbarry(AT)wit.ie), Dec 23 2004
O.g.f.: (1-4*x)/(-1+2*x+x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 15 2008
a(n)=first binomial transform of 2,1,4,2,8... [From Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009]
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MAPLE
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f:=proc(n) option remember; if n=0 then RETURN(-1); fi; if n=1 then RETURN(2); fi; 2*f(n-1)+f(n-2); end;
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MATHEMATICA
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a=2; b=3; lst={-1, a, b}; Do[c=(a+b)+b; AppendTo[lst, c]; a=b; b=c, {n, 3*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 13 2009]
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CROSSREFS
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Cf. A000129.
Sequence in context: A166302 A100342 A041281 this_sequence A148038 A148039 A148040
Adjacent sequences: A078340 A078341 A078342 this_sequence A078344 A078345 A078346
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KEYWORD
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sign
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 22 2002
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EXTENSIONS
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Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Apr 29 2004
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