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Search: id:A033539
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| A033539 |
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a(0)=1, a(1)=1, a(2)=1, a(n)=2*a(n-1)+a(n-2)+1. |
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+0
2
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| 1, 1, 1, 4, 10, 25, 61, 148, 358, 865, 2089, 5044, 12178, 29401, 70981, 171364, 413710, 998785, 2411281, 5821348, 14053978, 33929305, 81912589, 197754484, 477421558, 1152597601, 2782616761, 6717831124, 16218279010, 39154389145
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Number of times certain simple recursive programs call themselves.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..300
A. Karttunen, More information
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FORMULA
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a(n)=(3/4)*(1+sqrt(2))^(n-1)+3/4*(1-sqrt(2))^(n-1)-1/2+3*0^n, with n>=0 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 10 2009]
G.f.: (1-2*x-x^2+3*x^3)/(1-3*x+x^2+x^3) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 09 2009]
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PROGRAM
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(PARI) rev(n)=cnt++; if(n<=2, n >= 0, rev(n-1); rev(n-2); rev(n-1); 1); for(n=0, 50, cnt=0; print(n" "rev(n)" "cnt))
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CROSSREFS
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Cf. A033538.
Sequence in context: A111207 A113412 A159297 this_sequence A020748 A021004 A020709
Adjacent sequences: A033536 A033537 A033538 this_sequence A033540 A033541 A033542
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Antti Karttunen
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