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A091001 Number of walks of length n between adjacent nodes on the Petersen graph. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 22 14:46 EDT 2019. Contains 325224 sequences. (Running on oeis4.)