|
|
A033193
|
|
Binomial transform of A033192.
|
|
1
|
|
|
1, 2, 6, 19, 62, 207, 704, 2430, 8486, 29903, 106098, 378391, 1354700, 4863834, 17499302, 63055947, 227465414, 821215295, 2966571096, 10721076118, 38757594758, 140143505031, 506827217210, 1833150646599
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 10 and |s(i) - s(i-1)| = 1 for i = 1,2,...,2n, s(0) = 3, s(2n) = 3. - Herbert Kociemba, Jun 16 2004
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (x^4-7*x^3+11*x^2-6*x+1)/((1-3*x+x^2)*(1-5*x+5*x^2)).
a(n) = (1/5)*Sum_{r=1..9} sin(3*r*Pi/10)^2*(2*cos(r*Pi/10))^(2*n), n >= 1. - Herbert Kociemba, Jun 16 2004
|
|
MATHEMATICA
|
CoefficientList[Series[(x^4 - 7 x^3 + 11 x^2 - 6 x + 1)/((1 - 3 x + x^2) (1 - 5 x + 5 x^2)), {x, 0, 23}], x] (* Michael De Vlieger, Feb 12 2022 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|