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 A171231 #49 Nov 25 2024 04:25:55
%S A171231 2,4,7,14,27,54,107,214,427,854,1707,3414,6827,13654,27307,54614,
%T A171231 109227,218454,436907,873814,1747627,3495254,6990507,13981014,
%U A171231 27962027,55924054,111848107,223696214,447392427,894784854,1789569707
%N A171231 a(n) = (10*2^n + 3 - (-1)^n)/6.
%C A171231 From 14, the last 2 digits are of period 4: repeat [14, 27, 54, 07]. - _Paul Curtz_, Nov 22 2024
%H A171231 Vincenzo Librandi, <a href="/A171231/b171231.txt">Table of n, a(n) for n = 0..1000</a>
%H A171231 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).
%F A171231 a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3), n >= 3.
%F A171231 a(n+1) - a(n) = A048573(n-1).
%F A171231 a(n) = 2*A000975(n+1) - 3*A000975(n-1).
%F A171231 a(n) - a(n-2) = 5*2^n.
%F A171231 a(n+1) - 2*a(n) = ((-1)^n-1)/2 = -A000035(n).
%F A171231 G.f.: ( 2-3*x^2 ) / ( (x-1)*(2*x-1)*(1+x) ). - _R. J. Mathar_, Jul 07 2011
%F A171231 a(n) = ceiling( (5/3)*(2^n) ). - _Wesley Ivan Hurt_, Jun 28 2013
%t A171231 LinearRecurrence[{2,1,-2},{2,4,7},40] (* _Harvey P. Dale_, Feb 11 2015 *)
%o A171231 (PARI) a(n)=(10<<n+3)\/6 \\ _Charles R Greathouse IV_, Jul 07 2011
%o A171231 (Magma) [( 10*2^n+3-(-1)^n )/6: n in [0..40]]; // _Vincenzo Librandi_, Aug 05 2011
%Y A171231 Cf. A000035, A000975, A048573, A136412 (1st bisection), 2*A136412 (2nd bisection).
%Y A171231 Cf. A010712, A160113.
%K A171231 nonn,easy
%O A171231 0,1
%A A171231 _Paul Curtz_, Dec 05 2009
%E A171231 Definition replaced by the Lava formula of 2009. Contents converted to formulas. - _R. J. Mathar_, Jul 07 2011