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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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3
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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; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Number of times certain simple recursive programs call themselves.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..300
A. Karttunen, More information
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FORMULA
| 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, Sep 10 2009]
G.f.: (1-2*x-x^2+3*x^3)/(1-3*x+x^2+x^3) [From Jaume Oliver Lafont, Sep 09 2009]
a(0)=1, a(1)=1, a(2)=1, a(3)=4, a(n)=3*a(n-1)-a(n-2)-a(n-3) [From Harvey P. Dale, Nov 20 2011]
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MATHEMATICA
| Join[{1}, RecurrenceTable[{a[0]==a[1]==1, a[n]==2a[n-1]+a[n-2]+1}, a, {n, 30}]] (* or *) LinearRecurrence[{3, -1, -1}, {1, 1, 1, 4}, 30] (* From Harvey P. Dale, Nov 20 2011 *)
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PROG
| (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))
(Haskell)
a033539 n = a033539_list !! n
a033539_list =
1 : 1 : 1 : (map (+ 1) $ zipWith (+) (tail a033539_list)
(map (2 *) $ drop 2 a033539_list))
-- Reinhard Zumkeller, Aug 14 2011
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CROSSREFS
| Cf. A033538.
Sequence in context: A111207 A113412 A159297 * A020748 A021004 A020709
Adjacent sequences: A033536 A033537 A033538 * A033540 A033541 A033542
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Antti Karttunen
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