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A002248
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Number of points on y^2+xy=x^3+x^2+x over GF(2^n).
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0
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2, 8, 14, 16, 22, 56, 142, 288, 518, 968, 1982, 4144, 8374, 16472, 32494, 65088, 131174, 263144, 525086, 1047376, 2094358, 4193912, 8393806, 16783200, 33550022, 67092488, 134210174, 268460656, 536911222
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This is a divisibility sequence; that is, if n divides m, then a(n) divides a(m). The point at infinity is counted also. [From T. D. Noe (noe(AT)sspectra.com), Mar 12 2009]
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LINKS
| Hugh Williams, R. K. Guy, Some fourth-order linear divisibility sequences, Intl. J. Number Theory vol. 7 (5) (2011) 1255-1277
Index to divisibility sequences
Index to sequences with linear recurrences with constant coefficients, signature (4,-7,8,-4).
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FORMULA
| a(n) = 2^n + 1 - b(n), b(n)=b(n-1)-2*b(n-2), b(1)=1, b(2)=-3. b(n)=A002249(n).
G.f.: -2*x*(-1+2*x^2) / ( (x-1)*(2*x-1)*(2*x^2-x+1) ).
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MATHEMATICA
| Needs["FiniteFields`"]; Table[cnt=1; (* 1 point at infinity *) f=Table[GF[2, n][IntegerDigits[i, 2, n]], {i, 0, 2^n-1}]; Do[If[y^2+x*y-x^3-x^2-x==0, cnt++ ], {x, f}, {y, f}]; cnt, {n, 6}] [From T. D. Noe (noe(AT)sspectra.com), Mar 12 2009]
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CROSSREFS
| Sequence in context: A106359 A077241 A066567 * A194278 A050619 A056715
Adjacent sequences: A002245 A002246 A002247 * A002249 A002250 A002251
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Iwan Duursma (duursma(AT)research.att.com)
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