A030517 Number of walks of length n between two vertices on an icosahedron at distance 1.

1, 2, 13, 52, 273, 1302, 6573, 32552, 163073, 813802, 4070573, 20345052, 101733073, 508626302, 2543170573, 12715657552, 63578483073, 317891438802, 1589458170573, 7947285970052, 39736434733073, 198682149251302, 993410770670573, 4967053731282552

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)

Mathematica

LinearRecurrence[{4, 10, -20, -25}, {1, 2, 13, 52}, 24] (* Jean-François Alcover, Jul 12 2021 *)

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