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Search: id:A033538
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| A033538 |
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a(0)=1, a(1)=1, a(n)=3*a(n-1)+a(n-2)+1. |
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+0
3
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| 1, 1, 5, 17, 57, 189, 625, 2065, 6821, 22529, 74409, 245757, 811681, 2680801, 8854085, 29243057, 96583257, 318992829, 1053561745, 3479678065, 11492595941, 37957465889, 125364993609, 414052446717, 1367522333761, 4516619448001
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of times certain simple recursive programs (such as the Lisp program shown) call themselves on an input of length n.
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REFERENCES
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E. Hyvonen and J. Seppanen, LISP-kurssi, Osa 6 (Funktionaalinen ohjelmointi), Prosessori 4/1983, pp. 48-50 (in Finnish).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
A. Karttunen, More information
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FORMULA
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O.g.f.: (1-3x+3x^2)/((1-x)(1-3x-x^2)). a(n)=(4*A006190(n+1)-8*A006190(n)-1)/3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 22 2008]
a(n)=-1/3+2/39*(3/2-1/2*sqrt(13))^n*sqrt(13)-2/39*sqrt(13)*(3/2+1/2*sqrt(13))^n+2/3 *(3/2-1/2*sqrt(13))^n+2/3*(3/2+1/2*sqrt(13))^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Sep 01 2008]
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MAPLE
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a := proc(n) option remember; if(n < 2) then RETURN(1); else RETURN(3*a(n-1)+a(n-2)+1); fi; end;
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PROGRAM
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(Lisp) (defun rewerse (lista) (cond ((null (cdr lista)) lista) (t (cons (car (rewerse (cdr lista))) (rewerse (cons (car lista) (rewerse (cdr (rewerse (cdr lista))))))))))
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CROSSREFS
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Cf. A033539.
Sequence in context: A145371 A112044 A027030 this_sequence A027093 A027032 A027095
Adjacent sequences: A033535 A033536 A033537 this_sequence A033539 A033540 A033541
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Antti Karttunen
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