%I A002663 M4152 N1725
%S A002663 0,0,0,0,1,6,22,64,163,382,848,1816,3797,7814,15914,32192,64839,
%T A002663 130238,261156,523128,1047225,2095590,4192510,8386560,16774891,
%U A002663 33551806,67105912,134214424,268431773,536866822,1073737298
%N A002663 2^n - C(n,0)- ... - C(n,3).
%D A002663 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002663 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002663 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 A002663 J. Eckhoff, Der Satz von Radon in konvexen Productstrukturen II, Monat. 
               f. Math., 73 (1969), 7-30.
%H A002663 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 A002663 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 A002663 G.f.: x^4/((1-2*x)*(1-x)^4).
%F A002663 a(n)=sum{k=0..n, C(n, k+4)} = sum{k=4..n, C(n, k)}; a(n)=2a(n-1)+C(n-1, 
               3). - Paul Barry (pbarry(AT)wit.ie), Aug 23 2004
%p A002663 A002663:=-1/(2*z-1)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 
               dissertation.]
%t A002663 a=1;lst={};s1=s2=s3=s4=0;Do[s1+=a;s2+=s1;s3+=s2;s4+=s3;AppendTo[lst,s4];
               a=a*2,{n,5!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Jan 10 2009]
%t A002663 Table[Sum[ Binomial[n + 4, k + 4], {k, 0, n}], {n, -4, 26}] [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]
%Y A002663 a(n)= A055248(n, 4). Partial sums of A002662.
%Y A002663 Cf. A000079, A000225, A000295, A002662, A002664, A035038-A035042.
%Y A002663 Sequence in context: A053739 A055797 A001925 this_sequence A099855 A003469 
               A027992
%Y A002663 Adjacent sequences: A002660 A002661 A002662 this_sequence A002664 A002665 
               A002666
%K A002663 nonn,easy
%O A002663 0,6
%A A002663 N. J. A. Sloane (njas(AT)research.att.com).