A199210 a(n) = (11*4^n + 1)/3.

4, 15, 59, 235, 939, 3755, 15019, 60075, 240299, 961195, 3844779, 15379115, 61516459, 246065835, 984263339, 3937053355, 15748213419, 62992853675, 251971414699, 1007885658795, 4031542635179, 16126170540715, 64504682162859

Offset: 0

Author

Vincenzo Librandi, Nov 04 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Amya Luo, Pattern Avoidance in Nonnesting Permutations, Undergraduate Thesis, Dartmouth College (2024). See p. 16.
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

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).

Programs

Magma

[(11*4^n+1)/3: n in [0..30]];

Mathematica

LinearRecurrence[{5,-4}, {4,15}, 31] (* G. C. Greubel, Jan 19 2023 *)

SageMath

[(11*4^n+1)/3 for n in range(31)] # G. C. Greubel, Jan 19 2023

Formula

a(n) = 4*a(n-1) - 1.

a(n) = 5*a(n-1) - 4*a(n-2).

G.f.: (4-5*x)/((1-x)*(1-4*x)). - Bruno Berselli, Nov 04 2011

E.g.f.: (1/3)*(11*exp(4*x) + exp(x)). - G. C. Greubel, Jan 19 2023