A074601 a(n) = 2^n + 6^n.

2, 8, 40, 224, 1312, 7808, 46720, 280064, 1679872, 10078208, 60467200, 362799104, 2176786432, 13060702208, 78364180480, 470185017344, 2821109972992, 16926659575808, 101559956930560, 609359740534784, 3656158441111552

Offset: 0

Author

Robert G. Wilson v, Aug 25 2002

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Wei Chen, Enumeration of Set Partitions Refined by Crossing and Nesting Numbers, MS Thesis, Department of Mathematics. Simon Fraser University, Fall 2014. Table 5.2, r=2.
• Takao Komatsu, Asymmetric Circular Graph with Hosoya Index and Negative Continued Fractions, arXiv:2105.08277 [math.CO], 2021.
• Index entries for linear recurrences with constant coefficients, signature (8,-12).

Crossrefs

Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600 - A074624.

Programs

Magma

[2^n + 6^n: n in [0..35]]; // Vincenzo Librandi, Apr 30 2011

Mathematica

Table[2^n + 6^n, {n, 0, 22}]

Formula

a(n) = 6*a(n-1) - 2^n = 8*a(n-1) - 12*a(n-2).

From Mohammad K. Azarian, Jan 02 2009: (Start)

G.f.: 1/(1-2*x) + 1/(1-6*x).

E.g.f.: e^(2*x) + e^(6*x). (End)