A193669 - OEIS

%I #23 Apr 07 2024 08:49:12

%S 1,1,1,1,0,0,0,0,-1,-2,-3,-4,-4,-4,-4,-4,-3,-1,2,6,10,14,18,22,25,26,

%T 24,18,8,-6,-24,-46,-71,-97,-121,-139,-147,-141,-117,-71,0,97,218,357,

%U 504,645,762,833,833,736,518,161,-343,-988,-1750,-2583,-3416,-4152

%N Expansion of o.g.f.(1-x^4)/(1-x+x^8).

%C The Gi1 sums, see A180662, of triangle A108299 equal the terms of this sequence.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,-1).

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

%F a(n) = a(n-1) - a(n-8),  a(0) = a(1) = a(2) = a(3) = 1, a(4) = a(5) = a(6) = a(7) = 0.

%p A193669 := proc(n) option remember: coeftayl((1-x^4) / (1-x+x^8) ,x=0,n) end: seq(A193669(n), n=0..57);

%t CoefficientList[Series[(1-x^4)/(1-x+x^8),{x,0,80}],x] (* or *) LinearRecurrence[ {1,0,0,0,0,0,0,-1},{1,1,1,1,0,0,0,0},80] (* _Harvey P. Dale_, Jul 16 2014 *)

%Y Cf. A108299, A180662.

%K sign,easy

%O 0,10

%A _Johannes W. Meijer_, Aug 11 2011