Search: id:A005287
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%I A005287 M3894
%S A005287 5,20,49,98,174,285,440,649,923,1274,1715,2260,2924,3723,4674,5795,
%T A005287 7105,8624,10373,12374,14650,17225,20124,23373,26999,31030,35495,40424,
%U A005287 45848,51799,58310,65415,73149,81548,90649,100490,111110,122549,134848
%N A005287 Number of permutations of [n] with four inversions.
%D A005287 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005287 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 A005287 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 255, #2, b(n,4).
%D A005287 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied 
               Tables, Cambridge, 1966, p. 241.
%D A005287 R. K. Guy, personal communication.
%D A005287 R. H. Moritz and R. C. Williams, A coin-tossing problem and some related 
               combinatorics, Math. Mag., 61 (1988), 24-29.
%D A005287 E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, 
               p. 96.
%D A005287 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, 1999; see 
               Exercise 1.30, p. 49.
%H A005287 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 A005287 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 A005287 n*(n+1)*(n^2+n-14)/24
%F A005287 binomial(n,4)+binomial(n,3)-binomial(n,2), n>=5. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 23 2006
%e A005287 [2, 4, 3, 1], [3, 2, 4, 1], [3, 4, 1, 2], [4, 1, 3, 2], [4, 2, 1, 3] 
               have 4 inversions.
%p A005287 [seq(binomial(n,4)+binomial(n,3)-binomial(n,2), n=5..43)]; - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jul 23 2006
%p A005287 A005287:=(-5+5*z+z**2-3*z**3+z**4)/(z-1)**5; [Conjectured by S. Plouffe 
               in his 1992 dissertation.]
%p A005287 seq(sum(binomial(n,m), m=1..4)-n^2,n=5..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 19 2008
%o A005287 (PARI) a(n)=if(n<4,0,n*(n+1)*(n^2+n-14)/24)
%Y A005287 Cf. A008302.
%Y A005287 Sequence in context: A061188 A033429 A147002 this_sequence A147488 A134481 
               A062158
%Y A005287 Adjacent sequences: A005284 A005285 A005286 this_sequence A005288 A005289 
               A005290
%K A005287 nonn,easy
%O A005287 4,1
%A A005287 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
%E A005287 Additional comments from Michael Somos, Jun 25, 2002.

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