A384614 Expansion of (1+x+x^2) / (1-x-3*x^2).

1, 2, 6, 12, 30, 66, 156, 354, 822, 1884, 4350, 10002, 23052, 53058, 122214, 281388, 648030, 1492194, 3436284, 7912866, 18221718, 41960316, 96625470, 222506418, 512382828, 1179902082, 2717050566, 6256756812, 14407908510, 33178178946, 76401904476, 175936441314

Offset: 0

Author

Sean A. Irvine, Jun 04 2025

Keywords

• nonn
• easy
• walk

Comments

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

0-1

|\

| 2

|/

4-3.

Examples

			a(2)=6 because we have the walks 2-1-0, 2-1-2, 2-1-3, 2-3-1, 2-3-2, 2-3-4.
		

Links

• Sean A. Irvine, Walks on Graphs.

Crossrefs

Cf. A105476 (vertices 0, 1), A382683 (missing edge {4,3}).

Programs

Maple

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

Mathematica

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