%I A002664 M4395 N1851
%S A002664 0,0,0,0,0,1,7,29,93,256,638,1486,3302,7099,14913,30827,63019,127858,
%T A002664 258096,519252,1042380,2089605,4185195,8377705,16764265,
%U A002664 33539156,67090962,134196874,268411298,536843071,1073709893
%N A002664 2^n - C(n,0)- ... - C(n,4).
%D A002664 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002664 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002664 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A002664 J. Eckhoff, Der Satz von Radon in konvexen Productstrukturen II, Monat. 
               f. Math., 73 (1969), 7-30.
%H A002664 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A002664 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A002664 G.f.: x^5/((1-2*x)*(1-x)^5).
%F A002664 a(n)=sum{k=0..n, C(n, k+5)} = sum{k=5..n, C(n, k)}; a(n)=2a(n-1)+C(n-1, 
               4). - Paul Barry (pbarry(AT)wit.ie), Aug 23 2004
%p A002664 a:=n->sum(binomial(n,2*j),j=3..n): seq(a(n), n=1..31); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), May 12 2007
%p A002664 A002664:=1/(2*z-1)/(z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]
%t A002664 a=1;lst={};s1=s2=s3=s4=s5=0;Do[s1+=a;s2+=s1;s3+=s2;s4+=s3;s5+=s4;AppendTo[lst,
               s5];a=a*2,{n,5!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Jan 10 2009]
%t A002664 Table[Sum[ Binomial[n + 5, k + 5], {k, 0, n}], {n, -5, 25}] [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]
%Y A002664 a(n) = A055248(n, 5). Partial sums of A002663.
%Y A002664 Cf. A000079, A000225, A000295, A002662, A002663, A035038-A035042.
%Y A002664 Sequence in context: A001779 A053295 A055798 this_sequence A042609 A002941 
               A102485
%Y A002664 Adjacent sequences: A002661 A002662 A002663 this_sequence A002665 A002666 
               A002667
%K A002664 nonn,easy
%O A002664 0,7
%A A002664 N. J. A. Sloane (njas(AT)research.att.com).