This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A081250 #34 Jan 29 2025 15:06:22
%S A081250 1,3,11,33,101,303,911,2733,8201,24603,73811,221433,664301,1992903,
%T A081250 5978711,17936133,53808401,161425203,484275611,1452826833,4358480501,
%U A081250 13075441503,39226324511,117678973533,353036920601,1059110761803
%N A081250 Numbers k such that A081249(m)/m^2 has a local minimum for m = k.
%C A081250 The limit of the local minima, lim_{n->infinity} A081249(n)/n^2 = 1/10. For local maxima cf. A081251.
%H A081250 Vincenzo Librandi, <a href="/A081250/b081250.txt">Table of n, a(n) for n = 0..300</a>
%H A081250 Klaus Brockhaus, <a href="/A081134/a081134.gif">Illustration for A081134, A081249, A081250 and A081251</a>
%H A081250 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-3).
%F A081250 a(n) = floor(3^n*5/4).
%F A081250 G.f.: x*(1+x^2)/((1-x)*(1+x)*(1-3*x)).
%F A081250 a(n) = 3*a(n-1) + 1*a(n-2) - 3*a(n-3).
%F A081250 a(n) = (5*3^n + (-1)^n - 2)/4. - _Paul Barry_, May 19 2003
%F A081250 a(n) = a(n-2) + 10*3^(n-2) for n > 1.
%F A081250 a(n+2) - a(n) = A005052(n).
%F A081250 a(2*n) = Sum_{j=1..n+1} A062107(2*j).
%F A081250 a(2*n+1) = Sum_{j=1..n+1} A062107(2*j+1).
%F A081250 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
%F A081250 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
%F A081250 a(n) = 2*a(n-1) + 3*a(n-2) + 2, a(0)=1, a(1)=3. - _Zerinvary Lajos_, Apr 28 2008
%e A081250 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.
%p A081250 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..30); # _Zerinvary Lajos_, Apr 28 2008
%t A081250 Floor[5*3^Range[0, 30]/4] (* _Wesley Ivan Hurt_, Mar 30 2017 *)
%o A081250 (Magma) [Floor(3^n*5/4): n in [0..30]]; // _Vincenzo Librandi_, Jun 10 2011
%o A081250 (PARI) vector(30, n, n--; (5*3^n +(-1)^n -2)/4) \\ _G. C. Greubel_, Jul 14 2019
%o A081250 (Sage) [(5*3^n +(-1)^n -2)/4 for n in (0..30)] # _G. C. Greubel_, Jul 14 2019
%o A081250 (GAP) List([0..30], n-> (5*3^n +(-1)^n -2)/4); # _G. C. Greubel_, Jul 14 2019
%Y A081250 Cf. A005052, A062107, A081134, A081249, A081251.
%K A081250 nonn,easy
%O A081250 0,2
%A A081250 _Klaus Brockhaus_, Mar 17 2003
%E A081250 Offset changed from 1 to 0 by _Vincenzo Librandi_, Jun 10 2011