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A030517 Number of walks of length n between two vertices on a icosahedron at distance 1. 3
1, 2, 13, 52, 273, 1302, 6573, 32552, 163073, 813802, 4070573, 20345052, 101733073, 508626302, 2543170573, 12715657552, 63578483073, 317891438802, 1589458170573, 7947285970052, 39736434733073, 198682149251302, 993410770670573, 4967053731282552 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,10,-20,-25).

FORMULA

a(n) = 2*a(n-1) + 2*A030518(n-1) + 5*a(n-2).

A030518(n) = 2*a(n-1) + 2*A030518(n-1) + 5*A030518(n-2).

From Emeric Deutsch, Apr 03 2004: (Start)

a(n) = 5^n/12 - (-1)^n/12 + (sqrt(5))^(n+1)/20 + (-sqrt(5))^(n+1)/20.

a(n) = 4*a(n-1) + 10*a(n-2) - 20*a(n-3) - 25*a(n-4) for n>=5. (End)

From Colin Barker, Oct 17 2016: (Start)

G.f.: x*(1 - 2*x - 5*x^2)/((1 + x)*(1 - 5*x)*(1 - 5*x^2)).

a(n) = (5^n - 1)/12 for n even.

a(n) = (6*5^((n-1)/2) + 5^n + 1)/12 for n odd. (End)

PROG

(PARI) Vec(x*(1-2*x-5*x^2)/((1+x)*(1-5*x)*(1-5*x^2)) + O(x^30)) \\ Colin Barker, Oct 17 2016

CROSSREFS

Cf. A030518.

Sequence in context: A241892 A037383 A034476 * A048502 A177077 A144235

Adjacent sequences:  A030514 A030515 A030516 * A030518 A030519 A030520

KEYWORD

nonn,walk,easy

AUTHOR

Yasutoshi Kohmoto

STATUS

approved

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Last modified January 23 02:33 EST 2019. Contains 319365 sequences. (Running on oeis4.)