login
Expansion of (1-11x)/((1-x)(1-16x)).
2

%I #19 Jun 01 2020 07:40:16

%S 1,6,86,1366,21846,349526,5592406,89478486,1431655766,22906492246,

%T 366503875926,5864062014806,93824992236886,1501199875790166,

%U 24019198012642646,384307168202282326,6148914691236517206

%N Expansion of (1-11x)/((1-x)(1-16x)).

%C With interpolated zeros, this is the multinomial expression sum{i=0..n,sum{j=0..n,sum{k=0..n,if (mod(n-2i-4j-4k,6)=0,n!/(i!j!k!(n-i-j-k)!),0)}}}. Binomial transform of A091882.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16).

%F a(n) = 16^n/3 + 2/3; a(n) = A001045(4*n) + 1.

%F a(0)=1, a(1)=6, a(n) = 17*a(n-1) - 16*a(n-2) [_Harvey P. Dale_, Dec 15 2011]

%F a(n) = A078008(4n). - _Oboifeng Dira_, May 29 2020

%t CoefficientList[Series[(1-11x)/((1-x)(1-16x)),{x,0,30}],x] (* or *) LinearRecurrence[{17,-16},{1,6},30] (* _Harvey P. Dale_, Dec 15 2011 *)

%Y Cf. A001045, A078008, A091882.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Feb 10 2004