A384634 Expansion of (1+2*x+x^2) / (1-6*x^2-4*x^3+2*x^4).

1, 2, 7, 16, 48, 120, 338, 880, 2412, 6392, 17316, 46240, 124640, 333920, 898168, 2409600, 6475408, 17382432, 46694512, 125377024, 336745984, 904275328, 2428594976, 6521881856, 17515179200, 47037120384, 126321412672, 339239675392, 911046599168, 2446649462272

Offset: 0

Author

Sean A. Irvine, Jun 05 2025

Keywords

• nonn
• easy
• walk

Comments

Number of walks of length n starting at vertex 2 in the following graph:

2

/ \

0-1---3

\ /

4.

Examples

			a(2)=7 because we have the walks 2-1-0, 2-1-2, 2-1-3, 2-1-4, 2-3-1, 2-3-2, 2-3-4.
		

Links

• Sean A. Irvine, Walks on Graphs.
• Index entries for linear recurrences with constant coefficients, signature (0,6,4,-2).

Crossrefs

Cf. A384633 (vertices 0, 1), A384635 (vertex 3), A005824 (missing edge {1,3}), A105476 (missing edge {1,2}).

Programs

Maple

a:= n-> (<<0|1|0|0|0>, <1|0|1|1|1>, <0|1|0|1|0>, <0|1|1|0|1>, <0|1|0|1|0>>^n. <<1,1,1,1,1>>)[3,1]:
seq(a(n), n=0..32);

Mathematica

CoefficientList[Series[(1+2*x+x^2) / (1-6*x^2-4*x^3+2*x^4), {x, 0, 32}], x]