%I #8 Jun 13 2015 00:51:29

%S 1,7,41,227,1221,6447,33601,173467,889181,4533287,23015961,116477907,

%T 587981941,2962279327,14900875121,74862289547,375743103501,

%U 1884442140567,9445117195081,47317211944387,236952563597861

%N Expansion of (1-3x)/((1-x)(1-4x)(1-5x)).

%C Partial sums of A085351. Convolution of A034478 and 4^n. Convolution of A047849 and 5^n. a(n)=A097162(2n+1)/3. Third binomial transform of A097164.

%H <a href= "/index/Rec#order_03" >Index entries for linear recurrences with constant coefficients</a>, signature (10,-29,20).

%F a(n)=5*5^n/2-4*4^n/3-1/6; a(n)=sum{k=0..n, (5^k+1)4^(n-k)/2}; a(n)=sum{k=0..n, (4^k+2)5^(n-k)/3}; a(n)=10a(n-1)-29a(n-2)+20a(n-3).

%t CoefficientList[Series[(1-3x)/((1-x)(1-4x)(1-5x)),{x,0,30}],x] (* or *) LinearRecurrence[{10,-29,20},{1,7,41},30] (* _Harvey P. Dale_, Jan 24 2012 *)

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jul 30 2004