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Binomial transform of A033192.
1

%I #18 Feb 12 2022 23:46:59

%S 1,2,6,19,62,207,704,2430,8486,29903,106098,378391,1354700,4863834,

%T 17499302,63055947,227465414,821215295,2966571096,10721076118,

%U 38757594758,140143505031,506827217210,1833150646599

%N Binomial transform of A033192.

%C 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

%H Michael De Vlieger, <a href="/A033193/b033193.txt">Table of n, a(n) for n = 0..1791</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F G.f.: (x^4-7*x^3+11*x^2-6*x+1)/((1-3*x+x^2)*(1-5*x+5*x^2)).

%F 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

%t 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 *)

%Y Cf. A033192.

%K nonn

%O 0,2

%A _N. J. A. Sloane_