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