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A038521
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Number of elements of GF(2^n) with trace 1 and subtrace 1.
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4
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0, 2, 1, 4, 10, 12, 36, 64, 120, 272, 496, 1024, 2080, 4032, 8256, 16384, 32640, 65792, 130816, 262144, 524800, 1047552, 2098176, 4194304, 8386560, 16781312, 33550336, 67108864, 134225920, 268419072, 536887296, 1073741824, 2147450880
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| K. Cattel, C. R. Miers, F. Ruskey, J. Sawada, M. Serra, The number of irreducible polynomials over Gf(2) with given trace and subtrace, J. Combin. Math. Combin. Comput. 47 (2003) 31-64. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 20 2008]
F. Ruskey, Number of irreducible polynomials over GF(2) with given trace and subtrace
F. Ruskey, Number of elements of GF(2^n) of given trace and subtrace
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FORMULA
| C(n, r+0)+C(n, r+4)+C(n, r+8)+... where r = 3 if n odd, r = 1 if n even.
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MAPLE
| A038521 := proc(n) local r, a, i ; if n mod 2 = 1 then r := 3 ; else r := 1 ; fi; a :=0 ; for i from r to n by 4 do a := a+binomial(n, i) ; od; a ; end: for n from 1 to 40 do printf("%d, ", A038521(n)) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 20 2008]
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CROSSREFS
| Cf. A038504, A000749.
Cf. A038518, A038519, A038520.
Cf. A134654. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 20 2008]
Sequence in context: A038195 A205855 * A134654 A198262 A085421 A001071
Adjacent sequences: A038518 A038519 A038520 * A038522 A038523 A038524
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KEYWORD
| easy,nonn
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AUTHOR
| Frank Ruskey (ruskey(AT)cs.uvic.ca)
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EXTENSIONS
| Values duplicated A038520 and were replaced by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 20 2008
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