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A030518 Number of walks of length n between two vertices on a icosahedron at distance 2. 3
0, 2, 8, 52, 248, 1302, 6448, 32552, 162448, 813802, 4067448, 20345052, 101717448, 508626302, 2543092448, 12715657552, 63578092448, 317891438802, 1589456217448, 7947285970052, 39736424967448, 198682149251302, 993410721842448, 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*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

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)