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 A002248 Number of points on y^2+xy=x^3+x^2+x over GF(2^n). 2
 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; text; internal format)
 OFFSET 1,1 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, Mar 12 2009] LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Hugh Williams, R. K. Guy, Some fourth-order linear divisibility sequences, Intl. J. Number Theory vol. 7 (5) (2011) 1255-1277 Index entries for linear recurrences with constant coefficients, signature (4,-7,8,-4). 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) ). a(n) = 4*a(n-1) -7*a(n-2) +8*a(n-3) -4*a(n-4). Vincenzo Librandi, Jun 18 2012 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, Mar 12 2009] LinearRecurrence[{4, -7, 8, -4}, {2, 8, 14, 16}, 30] (* Vincenzo Librandi, Jun 18 2012 *) PROG (MAGMA) I:=[2, 8, 14, 16]; [n le 4 select I[n] else 4*Self(n-1)-7*Self(n-2)+8*Self(n-3)-4*Self(n-4): n in [1..45]]; // Vincenzo Librandi, Jun 18 2012 CROSSREFS Sequence in context: A077241 A228469 A066567 * A194278 A050619 A056715 Adjacent sequences:  A002245 A002246 A002247 * A002249 A002250 A002251 KEYWORD nonn,easy AUTHOR STATUS approved

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