A384611 Expansion of (1+2*x-x^3) / (1-5*x^2+2*x^4).

1, 2, 5, 9, 23, 41, 105, 187, 479, 853, 2185, 3891, 9967, 17749, 45465, 80963, 207391, 369317, 946025, 1684659, 4315343, 7684661, 19684665, 35053987, 89792639, 159900613, 409593865, 729395091, 1868384047, 3327174229, 8522732505, 15177080963, 38876894431

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:

2

/ \

0-1 3

\ /

4.

Examples

			a(3)=9 because we have the walks 2-1-0-1, 2-1-2-1, 2-1-2-3, 2-1-4-1, 2-1-4-3, 2-3-2-1, 2-3-2-3, 2-3-4-1, 2-3-4-3.
		

Links

• Sean A. Irvine, Walks on Graphs.
• Index entries for linear recurrences with constant coefficients, signature (0,5,0,-2).

Crossrefs

Cf. A005824 (vertices 0, 1), A079162 (vertex 3), A000079 (missing edge {0,1}).

Programs

Maple

a:= n-> (<<0|1|0|0|0>, <1|0|1|0|1>, <0|1|0|1|0>, <0|0|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^3) / (1-5*x^2+2*x^4), {x, 0, 32}], x]