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 A198643 #27 Aug 29 2024 15:43:22 %S A198643 4,14,44,134,404,1214,3644,10934,32804,98414,295244,885734,2657204, %T A198643 7971614,23914844,71744534,215233604,645700814,1937102444,5811307334, %U A198643 17433922004,52301766014,156905298044,470715894134,1412147682404,4236443047214 %N A198643 a(n) = 5*3^n-1. %H A198643 Vincenzo Librandi, <a href="/A198643/b198643.txt">Table of n, a(n) for n = 0..1000</a> %H A198643 Amya Luo, <a href="https://math.dartmouth.edu/theses/undergrad/2024/Luo-thesis.pdf">Pattern Avoidance in Nonnesting Permutations</a>, Undergraduate Thesis, Dartmouth College (2024). See p. 11. %H A198643 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3). %F A198643 a(n) = 3*a(n-1)+2 = 2*A060816(n+1). %F A198643 G.f.: ( 4-2*x ) / ( (3*x-1)*(x-1) ). - _R. J. Mathar_, Nov 17 2011 %t A198643 5*3^Range[0, 30] - 1 (* or *) %t A198643 NestList[3*# + 2 &, 4, 30] (* _Paolo Xausa_, Aug 28 2024 *) %o A198643 (Magma) [5*3^n-1: n in [0..30]]; %o A198643 (PARI) a(n)=5*3^n-1 \\ _Charles R Greathouse IV_, Oct 07 2015 %Y A198643 Cf. A027107, A048473, A171498. %K A198643 nonn,easy %O A198643 0,1 %A A198643 _Vincenzo Librandi_, Oct 28 2011