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%I
%S 1,3,10,35,126,463,1730,6555,25126,97223,379050,1486675,5858126,
%T 23166783,91869970,365088395,1453179126,5791193143,23100202490,
%U 92207099715,368247268126,1471245680303,5879752544610,23503319648635
%N Expansion of (1-5*x+5*x^2)/((1-x)*(1-3*x)*(1-4*x)).
%C Binomial transform of A085281.
%C Number of walks of length 2n+1 between two adjacent vertices in the cycle graph C_12. - _Herbert Kociemba_, Jul 05 2004
%H Vincenzo Librandi, <a href="/A085282/b085282.txt">Table of n, a(n) for n = 0..500</a>
%H Mircea Merca, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL15/Merca1/merca6.html">A Note on Cosine Power Sums</a> J. Integer Sequences, Vol. 15 (2012), Article 12.5.3.
%F a(n)=4^n/3+3^n/2+1/6
%F a(n) = sum(binomial(2*n,n+6*k)/2, k=-floor(n/6)..floor(n/6)). [_Mircea Merca_, Jan 28 2012]
%o (MAGMA) [4^n/3+3^n/2+1/6: n in [0..35]]; // Vincenzo Librandi, May 29 2011
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jun 25 2003
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