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A081250
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Numbers n such that A081249(m)/m^2 has a local minimum for m = n.
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11
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1, 3, 11, 33, 101, 303, 911, 2733, 8201, 24603, 73811, 221433, 664301, 1992903, 5978711, 17936133, 53808401, 161425203, 484275611, 1452826833, 4358480501, 13075441503, 39226324511, 117678973533, 353036920601, 1059110761803
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OFFSET
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0,2
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COMMENTS
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The limit of the local minima, lim A081249(n)/n^2 = 1/10. For local maxima cf. A081251.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..300
Klaus Brockhaus, Illustration for A081134, A081249, A081250 and A081251
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FORMULA
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a(n) = floor(3^n*5/4).
G.f.: x*(1+x^2)/((1-x)*(1+x)*(1-3*x)).
a(n) = +3*a(n-1) +1*a(n-2) -3*a(n-3).
a(n)=5*3^n/4 + (-1)^n/4-1/2. - Paul Barry, May 19 2003
a(n) = a(n-2) + 10*3^(n-2) for n > 1.
a(n+2) - a(n) = A005052(n).
a(2*n) = sum(j=1..n+1, A062107(2*j) ); a(2*n+1) = sum(j=1..n+1, A062107(2*j+1) ).
With a leading 0, this is a(n)=(5*3^n-6+4*0^n-3*(-1)^n)/12, the binomial transform of A084183. - Paul Barry, May 19 2003
Convolution of 3^n and {1, 0, 2, 0, 2, 0, ....}. a(n)=sum{k=0..n, ((1+(-1)^k)-0^k)3^(n-k)}=sum{k=0..n, ((1+(-1)^(n-k))-0^(n-k))3^k} - Paul Barry, Jul 19 2004
a(n)=2*a(n-1)+3*a(n-2)+2,a(0)=1, a(1)=3. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 28 2008
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EXAMPLE
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11 is a term since A081249(10)/10^2 = 11/100 = 0.110, A081249(11)/11^2 = 13/121 = 0.107, A081249(12)/12^2 = 16/144 = 0.111.
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MAPLE
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a[0]:=1:a[1]:=3:for n from 2 to 50 do a[n]:=2*a[n-1]+3*a[n-2]+2 od: seq(a[n], n=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 28 2008
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PROG
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(MAGMA) [Floor(3^n*5/4): n in [0..30]]; // Vincenzo Librandi, Jun 10 2011
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CROSSREFS
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Cf. A081134, A081249, A081251, A005052, A062107.
Sequence in context: A182879 A124640 A081673 * A135247 A094539 A032199
Adjacent sequences: A081247 A081248 A081249 * A081251 A081252 A081253
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus, Mar 17 2003
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EXTENSIONS
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Offset changed from 1 to 0 by Vincenzo Librandi, Jun 10 2011
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STATUS
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approved
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