A124751 - OEIS

%I #4 Mar 10 2017 13:26:57

%S 1,0,1,0,1,0,1,-1,1,-1,1,-1,1,-2,2,-2,2,-2,2,-3,4,-4,4,-4,4,-5,7,-8,8,

%T -8,8,-9,12,-15,16,-16,16,-17,21,-27,31,-32,32,-33,38,-48,58,-63,64,

%U -65,71,-86,106,-121,127,-129,136,-157,192,-227,248

%N Expansion of (1+x^2+x^4)/(1-x^6+x^7).

%C Diagonal sums of number triangle A124749.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1,-1).

%F a(n)=sum{k=0..floor(n/2), C(floor(k/3),n-2k)*(-1)^n}

%t CoefficientList[Series[(1+x^2+x^4)/(1-x^6+x^7),{x,0,100}],x] (* or *) LinearRecurrence[{0,0,0,0,0,1,-1},{1,0,1,0,1,0,1},100] (* _Harvey P. Dale_, Mar 10 2017 *)

%K easy,sign

%O 0,14

%A _Paul Barry_, Nov 06 2006