1,2

The limit of the local minima, lim A081249(n)/n^2 = 1/10. For local maxima cf. A081251.

Klaus Brockhaus, Illustration for A081134, A081249, A081250 and A081251

a(n) = floor(3^n*5/4).

a(n) = a(n-2) + 10*3^(n-2) for n > 1; a(n+2) - a(n) = A005052(n); a(2n) = sum{j=1..n+1, A062107(2*j)}, a(2n+1) = sum{j=1..n+1, A062107(2*j+1)}.

G.f.: (x^2 + 1)/((x - 1)*(x + 1)*(3*x - 1)).

a(n)=5*3^n/4 + (-1)^n/4-1/2. - Paul Barry (pbarry(AT)wit.ie), May 19 2003

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 (pbarry(AT)wit.ie), 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 (pbarry(AT)wit.ie), 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

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.

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

Cf. A081134, A081249, A081251, A005052, A062107.

Sequence in context: A079996 A124640 A081673 this_sequence A135247 A094539 A032199

Adjacent sequences: A081247 A081248 A081249 this_sequence A081251 A081252 A081253

nonn

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 17 2003