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A122743
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Number of normalized polynomials of degree n in GF(2)[x,y].
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5
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1, 6, 56, 960, 31744, 2064384, 266338304, 68451041280, 35115652612096, 35993612646875136, 73750947497819242496, 302157667927362455470080, 2475577847115856892504571904, 40562343327224770087344704323584
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)=(n-1)-st elementary symmetric function of {2,4,6,16,...,2^n); see Mathematica program.
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REFERENCES
| Arnaud Bodin, Number of irreducible polynomials in several variables over finite fields, http://arxiv.org/abs/0706.0157, Amer. Math. Monthly, 115 (2008), 653-660.
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FORMULA
| a(n) = 2^((n+1)(n+2)/2) - 2^(n(n+1)/2). [From Paul D. Hanna (pauldhanna(AT)juno.com), Apr 08 2009]
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EXAMPLE
| Let esf "abbreviate elementary symmetric function". Then
0th esf of {2} is 1.
1st efs of {2,4} is 2+4=6.
2nd efs of {2,4,8} is 2*4+2*8+4*8=56.
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MATHEMATICA
| f[k_] := 2^k; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 16}] (* A122743 *)
(* Clark Kimberling, Dec 29 2011 *)
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CROSSREFS
| Cf. A115457, A203011.
Row sums of powers of two triangle A000079.
Equals A000225(n+1)*2^A000217(n).
Sequence in context: A093197 A052317 A185524 * A137032 A053421 A083696
Adjacent sequences: A122740 A122741 A122742 * A122744 A122745 A122746
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 13 2008
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EXTENSIONS
| Edited, terms and links added by Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 10 2010
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