%I A006522 M3413
%S A006522 1,0,0,1,4,11,25,50,91,154,246,375,550,781,1079,1456,1925,2500,
%T A006522 3196,4029,5016,6175,7525,9086,10879,12926,15250,17875,20826,24129,
%U A006522 27811,31900,36425,41416,46904,52921,59500,66675,74481,82954,92131
%N A006522 4-dimensional analogue of centered polygonal numbers. Also number of 
               regions created by sides and diagonals of n-gon.
%D A006522 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006522 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 74, Problem 8.
%D A006522 J. W. Freeman, The number of regions determined by a convex polygon, 
               Math. Mag., 49 (1976), 23-25.
%D A006522 R. Honsberger, Mathematical Gems, M.A.A., 1973, p. 102.
%H A006522 Math Forum, <a href="http://mathforum.org/library/drmath/view/55262.html">
               Regions of a circle Cut by Chords to n points</a>.
%H A006522 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 A006522 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.
%H A006522 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PolygonDiagonal.html">Link to a section of The World of Mathematics.</
               a>
%F A006522 a(n)=binomial(n, 4)+ binomial(n-1, 2)
%F A006522 binomial(n,2)+binomial(n,3)+binomial(n,4), n>=-1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 23 2006
%e A006522 For a pentagon in general position, 11 regions are formed (Comtet, Fig. 
               20, p. 74).
%p A006522 A006522 := n->(1/24)*(n-1)*(n-2)*(n^2-3*n+12);
%p A006522 [seq(binomial(n,2)+binomial(n,3)+binomial(n,4), n=-1..40)]; - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jul 23 2006
%p A006522 A006522:=-(1-z+z**2)/(z-1)**5; [S. Plouffe in his 1992 dissertation. 
               Gives sequence except for three leading terms.]
%p A006522 seq(sum(binomial(n,k+1),k=1..3),n=-1..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Dec 14 2007
%t A006522 a=2;b=3;s=4;lst={1,0,0,1,s};Do[a+=n;b+=a;s+=b;AppendTo[lst,s],{n,2,6!,
               1}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 24 
               2009]
%Y A006522 Partial sums of A004006.
%Y A006522 Sequence in context: A110610 A051462 A006004 this_sequence A036837 A011851 
               A136395
%Y A006522 Adjacent sequences: A006519 A006520 A006521 this_sequence A006523 A006524 
               A006525
%K A006522 nonn,easy,nice
%O A006522 0,5
%A A006522 N. J. A. Sloane (njas(AT)research.att.com).