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A035039 2^n - C(n,0)- ... - C(n,6). 7

%I

%S 0,0,0,0,0,0,0,1,9,46,176,562,1586,4096,9908,22819,50643,109294,

%T 230964,480492,988116,2014992,4084248,8243109,16587165,33308926,

%U 66794952,133820134,267936278,536249296,1072973612,2146540999

%N 2^n - C(n,0)- ... - C(n,6).

%C a(n)= A055248(n,7). Partial sums of A035038.

%D J. Eckhoff, Der Satz von Radon in konvexen Productstrukturen II, Monat. f. Math., 73 (1969), 7-30.

%H <a href="/index/Rec#order_08">Index to sequences with linear recurrences with constant coefficients</a>, signature (9,-35,77,-105,91,-49,15,-2).

%F G.f.: x^7/((1-2*x)*(1-x)^7).

%F a(n)=sum{k=0..n, C(n, k+7)} = sum{k=7..n, C(n, k)}; a(n)=2a(n-1)+C(n-1, 6). - _Paul Barry_, Aug 23 2004

%p a:=n->sum(binomial(n,j),j=7..n): seq(a(n), n=0..31); - _Zerinvary Lajos_, Feb 12 2007

%t a=1;lst={};s1=s2=s3=s4=s5=s6=s7=0;Do[s1+=a;s2+=s1;s3+=s2;s4+=s3;s5+=s4;s6+=s5;s7+=s6;AppendTo[lst,s7];a=a*2,{n,5!}];lst [From _Vladimir Joseph Stephan Orlovsky_, Jan 10 2009]

%Y Cf. A000079, A000225, A000295, A002663, A002664, A035038-A035042.

%K nonn,easy

%O 0,9

%A _N. J. A. Sloane_.

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Last modified September 16 11:21 EDT 2014. Contains 246816 sequences.