A091001 Number of walks of length n between adjacent nodes on the Petersen graph.

0, 1, 0, 5, 4, 33, 56, 253, 588, 2105, 5632, 18261, 52052, 161617, 473928, 1443629, 4287196, 12948969, 38672144, 116365957, 348398820, 1046594561, 3136987480, 9416554845, 28238479724, 84737808793, 254168687136, 762595539893

Offset

0,4

References

N. Biggs, Algebraic Graph Theory, Cambridge, 2nd. Ed., 1993, p. 20.

F. Harary, Graph Theory, Addison-Wesley, 1969, p. 89.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,5,-6).

Formula

G.f.: x*(1-2*x)/((1-x)*(1+2*x)*(1-3*x)).

a(n) = (3^(n+1) + (-2)^(n+3) + 5)/30.

3^n = A091000(n) + 3*a(n) + 6*A091002(n).

a(n) = (A000244(n) - A001045(n+1)*(-1)^n - 6*A001045(n)*(-1)^n)/10.

a(n) = A091002(n+1) - 2*A091002(n). - R. J. Mathar, Oct 30 2014

E.g.f.: (3*exp(3*x) - 8*exp(-2*x) +5*exp(x))/30. - G. C. Greubel, Feb 01 2019

Mathematica

Table[(3^(n+1)+(-2)^(n+3)+5)/30, {n, 0, 30}] (* or *) LinearRecurrence[{2, 5, -6}, {0, 1, 0}, 30] (* G. C. Greubel, Feb 01 2019 *)

Prog

(PARI) vector(30, n, n--; (3^(n+1)+(-2)^(n+3)+5)/30) \\ G. C. Greubel, Feb 01 2019
(Magma) [(3^(n+1)+(-2)^(n+3)+5)/30: n in [0..30]]; // G. C. Greubel, Feb 01 2019
(Sage) [(3^(n+1)+(-2)^(n+3)+5)/30 for n in (0..30)] # G. C. Greubel, Feb 01 2019
(GAP) List([0..30], n -> (3^(n+1)+(-2)^(n+3)+5)/30) # G. C. Greubel, Feb 01 2019

Crossrefs

Sequence in context: A051138 A157101 A237648 * A297936 A298548 A078811

Adjacent sequences: A090998 A090999 A091000 * A091002 A091003 A091004

Keyword

easy,nonn

Author

Paul Barry, Dec 12 2003

Status

approved