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%I A199210 #22 Jun 12 2024 12:05:48
%S A199210 4,15,59,235,939,3755,15019,60075,240299,961195,3844779,15379115,
%T A199210 61516459,246065835,984263339,3937053355,15748213419,62992853675,
%U A199210 251971414699,1007885658795,4031542635179,16126170540715,64504682162859
%N A199210 a(n) = (11*4^n + 1)/3.
%H A199210 Vincenzo Librandi, <a href="/A199210/b199210.txt">Table of n, a(n) for n = 0..1000</a>
%H A199210 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. 16.
%H A199210 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F A199210 a(n) = 4*a(n-1) - 1.
%F A199210 a(n) = 5*a(n-1) - 4*a(n-2).
%F A199210 G.f.: (4-5*x)/((1-x)*(1-4*x)). - _Bruno Berselli_, Nov 04 2011
%F A199210 E.g.f.: (1/3)*(11*exp(4*x) + exp(x)). - _G. C. Greubel_, Jan 19 2023
%t A199210 LinearRecurrence[{5,-4}, {4,15}, 31] (* _G. C. Greubel_, Jan 19 2023 *)
%o A199210 (Magma) [(11*4^n+1)/3: n in [0..30]];
%o A199210 (SageMath) [(11*4^n+1)/3 for n in range(31)] # _G. C. Greubel_, Jan 19 2023
%Y A199210 Sequences of the form (m*4^n + 1)/3: A007583 (m=2), A136412 (m=5),  this sequence (m=11), A199210 (m=11), A206373 (m=14).
%K A199210 nonn,easy
%O A199210 0,1
%A A199210 _Vincenzo Librandi_, Nov 04 2011

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