%I A005286 M4109
%S A005286 1,6,15,29,49,76,111,155,209,274,351,441,545,664,799,951,1121,1310,
%T A005286 1519,1749,2001,2276,2575,2899,3249,3626,4031,4465,4929,5424,5951,
%U A005286 6511,7105,7734,8399,9101,9841,10620,11439,12299,13201,14146,15135
%N A005286 (n + 3)(n^2 + 6n + 2)/6.
%C A005286 Number of permutations of [n+3] with three inversions. - Michael Somos, 
               Jun 25, 2002
%D A005286 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005286 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 A005286 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 255, #2, b(n,3).
%D A005286 R. K. Guy, personal communication.
%D A005286 R. H. Moritz and R. C. Williams, A coin-tossing problem and some related 
               combinatorics, Math. Mag., 61 (1988), 24-29.
%D A005286 E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, 
               p. 96.
%D A005286 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, 1999; see 
               Exercise 1.30, p. 49.
%H A005286 T. D. Noe, <a href="b005286.txt">Table of n, a(n) for n=0..1000</a>
%H A005286 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 A005286 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 A005286 a(-6-n)=-a(n). - Michael Somos May 12 2005
%F A005286 binomial(n,3)+binomial(n,2)-n, n>=3. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 23 2006
%F A005286 G.f.: (1+2x-3x^2+x^3)/(1-x)^4. a(n) = a(n-1)+A000096(n+1) = A005581(n+2)-1. 
               - Henry Bottomley (se16(AT)btinternet.com), Oct 25 2001
%p A005286 [seq(binomial(n,3)+binomial(n,2)-n, n=3..45)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 23 2006
%p A005286 A005286:=(1+2*z-3*z**2+z**3)/(z-1)**4; [Conjectured by S. Plouffe in 
               his 1992 dissertation.]
%o A005286 (PARI) a(n)=n+=3; (n^3-7*n)/6 /* Michael Somos May 12 2005 */
%Y A005286 Cf. A008302.
%Y A005286 Sequence in context: A026102 A144519 A066995 this_sequence A025212 A024972 
               A048749
%Y A005286 Adjacent sequences: A005283 A005284 A005285 this_sequence A005287 A005288 
               A005289
%K A005286 nonn,easy,nice
%O A005286 0,2
%A A005286 N. J. A. Sloane (njas(AT)research.att.com).