%I A000128 M1120 N0428
%S A000128 1,2,4,8,16,31,58,105,185,319,541,906,1503,2476,4058,6626,10790,17537,
%T A000128 28464,46155,74791,121137,196139,317508,513901,831686,1345888,2177900,
%U A000128 3524140,5702419,9226966,14929821,24157253,39087571,63245353,102333486
%N A000128 A nonlinear binomial sum.
%D A000128 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000128 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000128 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 A000128 D. A. Lind, On a class of nonlinear binomial sums, Fib. Quart., 3 (1965), 
               292-298.
%H A000128 T. D. Noe, <a href="b000128.txt">Table of n, a(n) for n=1..201</a>
%H A000128 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 A000128 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 A000128 G.f.: (1 - 2 x + x^2 + x^3 ) / ( 1 - x - x^2 ) ( 1 - x )^3.
%F A000128 Fib(n+4) - n(n+1)/2 - 3, with Fib(n) = A000045(n). - Ralf Stephan, Aug 
               19 2004
%p A000128 A000128:=(1-2*z+z**2+z**3)/(z**2+z-1)/(z-1)**3; [Conjectured by S. Plouffe 
               in his 1992 dissertation.]
%Y A000128 Differences are A000126.
%Y A000128 Sequence in context: A056183 A000127 A133552 this_sequence A106399 A007800 
               A102726
%Y A000128 Adjacent sequences: A000125 A000126 A000127 this_sequence A000129 A000130 
               A000131
%K A000128 nonn,easy
%O A000128 1,2
%A A000128 N. J. A. Sloane (njas(AT)research.att.com).
%E A000128 More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Oct 06 2002