A030518 Number of walks of length n between two vertices on an icosahedron at distance 2.

0, 2, 8, 52, 248, 1302, 6448, 32552, 162448, 813802, 4067448, 20345052, 101717448, 508626302, 2543092448, 12715657552, 63578092448, 317891438802, 1589456217448, 7947285970052, 39736424967448, 198682149251302, 993410721842448, 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*A030517(n-1) + 2*a(n-1) + 5*a(n-2).

A030517(n) = 2*A030517(n-1) + 2*a(n-1) + 5*A030517(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). (End)

From Colin Barker, Oct 17 2016: (Start)

G.f.: 2*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) concat(0, Vec(2*x^2/((1+x)*(1-5*x)*(1-5*x^2)) + O(x^30))) \\ Colin Barker, Oct 17 2016

Crossrefs

Cf. A030517.

Sequence in context: A191480 A013555 A018987 * A123188 A027329 A136794

Adjacent sequences: A030515 A030516 A030517 * A030519 A030520 A030521

Keyword

nonn,walk,easy

Author

Yasutoshi Kohmoto

Status

approved