OFFSET
0,2
COMMENTS
Number of walks of length n starting at vertex 2 in the following graph:
2
/ \
0-1 3
\ /
4.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Sean A. Irvine, Walks on Graphs.
Index entries for linear recurrences with constant coefficients, signature (0,5,0,-2).
EXAMPLE
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.
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]
LinearRecurrence[{0, 5, 0, -2}, {1, 2, 5, 9}, 33] (* Vincenzo Librandi, Oct 14 2025 *)
PROG
(Magma) I:=[1, 2, 5, 9]; [n le 4 select I[n] else 5*Self(n-2)-2*Self(n-4): n in [1..35]]; // Vincenzo Librandi, Oct 14 2025
CROSSREFS
KEYWORD
nonn,easy,walk
AUTHOR
Sean A. Irvine, Jun 04 2025
STATUS
approved