|
%I #15 Jun 10 2018 20:51:47
%S 1,1,5,16,50,163,524,1687,5435,17503,56372,181558,584741,1883272,
%T 6065441,19534921,62915981,202633048,652618802,2101884691,6769524932,
%U 21802560343,70219349555,226154954935,728375639564,2345874192598,7555340168693,24333429833872
%N Expansion of (1-x)/(1-2*x-3*x^2-3*x^3).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 3, 3).
%F a(0)=1 and, for n >= 1, a(n) = Sum(k=1..n, Sum(i=k..n,(Sum(j=0..k, binomial(j,-3*k+2*j+i)*3^(-2*k+j+i)*binomial(k,j)))*binomial(n+k-i-1,k-1))). - _Vladimir Kruchinin_, May 05 2011
%F a(0)=1, a(1)=1, a(2)=5, a(n) = 2*a(n-1) + 3*a(n-2) + 3*a(n-3). - _Harvey P. Dale_, Aug 19 2014
%t CoefficientList[Series[(1-x)/(1-2x-3x^2-3x^3),{x,0,30}],x] (* or *) LinearRecurrence[{2,3,3},{1,1,5},30] (* _Harvey P. Dale_, Aug 19 2014 *)
%o (Maxima)
%o a(n):=sum(sum((sum(binomial(j,-3*k+2*j+i)*3^(-2*k+j+i)*binomial(k,j),j,0,k))*binomial(n+k-i-1,k-1),i,k,n),k,1,n); /* _Vladimir Kruchinin_, May 05 2011 */
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Nov 17 2002
|
