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A030518 Number of walks of length n between two vertices on an icosahedron at distance 2. 4
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
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
KEYWORD
nonn,walk,easy
AUTHOR
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)