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A005183
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n*2^(n-1) + 1.
(Formerly M1434)
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16
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1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689, 245761, 524289, 1114113, 2359297, 4980737, 10485761, 22020097, 46137345, 96468993, 201326593, 419430401, 872415233, 1811939329, 3758096385, 7784628225
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of permutations of length n which avoid the patterns 132, 4312. - Lara Pudwell (Lara.Pudwell(AT)valpo.edu), Jan 21 2006
a(n) = A000788(A000079(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2010]
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REFERENCES
| R. K. Guy, The second strong law of small numbers. Math. Mag. 63 (1990), no. 1, 3-20.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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.
Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.
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FORMULA
| Main diagonal of the array defined by T(0, j)=j+1 j>=0, T(i, 0)=i+1 i>=0, T(i, j)=T(i-1, j-1)+T(i-1, j)-1 - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 17 2003
G.f.: A(x) = -{x(3x^2-3x+1)}/{(x-1)(2x-1)^2} - Lara Pudwell (Lara.Pudwell(AT)valpo.edu), Jan 21 2006
Binomial transform of A028310. a(n)=1+sum{k=0..n, C(n, k)k}=1+A001787(n) - Paul Barry (pbarry(AT)wit.ie), Jul 21 2003
a(n) = sum(k=0, 2^n, A000120(k) ) = A000788(2^n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 25 2003
Row sums of triangle A134399 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2007
a(n)=2*a(n-1)+2^(n-1)-1 (with a(0)=1). [From Vincenzo Librandi, Dec 31 2010]
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MAPLE
| A005183:=-(1-3*z+3*z**2)/(z-1)/(-1+2*z)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[(n+1)*2^n+1, {n, 1, 30}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 09 2006
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CROSSREFS
| Cf. A134399.
Sequence in context: A027929 A001659 A088921 * A005348 A067676 A116703
Adjacent sequences: A005180 A005181 A005182 * A005184 A005185 A005186
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
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EXTENSIONS
| More terms from Lara Pudwell (Lara.Pudwell(AT)valpo.edu), Jan 21 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Jim Propp, Jul 14 2007
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