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Search: id:A005286
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| A005286 |
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(n + 3)(n^2 + 6n + 2)/6.
(Formerly M4109)
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+0
4
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| 1, 6, 15, 29, 49, 76, 111, 155, 209, 274, 351, 441, 545, 664, 799, 951, 1121, 1310, 1519, 1749, 2001, 2276, 2575, 2899, 3249, 3626, 4031, 4465, 4929, 5424, 5951, 6511, 7105, 7734, 8399, 9101, 9841, 10620, 11439, 12299, 13201, 14146, 15135
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of permutations of [n+3] with three inversions. - Michael Somos, Jun 25, 2002
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 255, #2, b(n,3).
R. K. Guy, personal communication.
R. H. Moritz and R. C. Williams, A coin-tossing problem and some related combinatorics, Math. Mag., 61 (1988), 24-29.
E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 96.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, 1999; see Exercise 1.30, p. 49.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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a(-6-n)=-a(n). - Michael Somos May 12 2005
binomial(n,3)+binomial(n,2)-n, n>=3. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 23 2006
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
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MAPLE
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[seq(binomial(n, 3)+binomial(n, 2)-n, n=3..45)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 23 2006
A005286:=(1+2*z-3*z**2+z**3)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROGRAM
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(PARI) a(n)=n+=3; (n^3-7*n)/6 /* Michael Somos May 12 2005 */
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CROSSREFS
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Cf. A008302.
Sequence in context: A026102 A144519 A066995 this_sequence A025212 A024972 A048749
Adjacent sequences: A005283 A005284 A005285 this_sequence A005287 A005288 A005289
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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