A384600 Expansion of (1+x-x^2) / (1-x-4*x^2+2*x^3+2*x^4).

1, 2, 5, 11, 25, 55, 123, 271, 603, 1331, 2955, 6531, 14483, 32035, 70995, 157107, 348051, 770419, 1706419, 3777779, 8366515, 18523955, 41021619, 90828851, 201134387, 445358643, 986195251, 2183703347, 4835498291, 10707203891, 23709399859, 52499812147

Offset: 0

Author

Sean A. Irvine, Jun 04 2025

Keywords

• nonn
• walk
• easy

Comments

Number of walks of length n on the following graph starting at vertex 3:

3

/|

0-1-2 |

\|

4.

Examples

			a(2)=5 because we have the walk 3-2-1, 3-2-3, 3-2-4, 3-4-2, 3-4-3.
		

Links

• Sean A. Irvine, Walks on Graphs.
• Index entries for linear recurrences with constant coefficients, signature (1,4,-2,-2).

Crossrefs

Cf. A384598 (vertices 0 and 1), A384599 (vertex 2), A062112 (missing edge {3,4}), A382683 (missing edge {0,1}).

Programs

Maple

a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <-2|-2|4|1>>^n. <<1,2,5,11>>)[1,1]:
seq(a(n), n=0..31);  # Alois P. Heinz, Jun 04 2025

Mathematica

CoefficientList[Series[(1 + x - x^2)/(1 - x - 4*x^2 + 2*x^3 + 2*x^4), {x, 0, 31}], x] (* Michael De Vlieger, Jun 04 2025 *)