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%I #12 Apr 06 2017 21:22:27
%S 3,7,15,31,63,127,217,511,1023,2047,3255,8001,11811,32767,63457,
%T 131071,262143,520065,1048575,2097151,4194303,8388607,16766977,
%U 33554431,67074049,133693185,268435455,536870911,1073215489,2147483647,4292868097,8589934591,17179312129
%N Maximal order of the trinomials of degree n over GF(2).
%C a(n) is also the maximum length of binary linear recurrence relation b(x) = b(x-m) + b(x-n) mod 2 for all 0 < m < n. Knuth cites unpublished work of G. J. Mitchell & D. P. Moore showing that a(55) = 2^55 - 1 via m = 24.
%D D. E. Knuth, The Art of Computer Programming. Vol. 2, Seminumerical Algorithms.
%H Hiroaki Yamanouchi, <a href="/A283091/b283091.txt">Table of n, a(n) for n = 2..100</a>
%H <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers.</a>
%F a(n) <= 2^n - 1, with equality if and only if n is a term of A073726.
%o (PARI) isperiodic(v)=for(k=1,#v-3, for(i=k+1,#v, if(v[i]!=v[i-k], next(2))); return(k))
%o T(n,m,len=2^n+7)=my(v=vectorsmall(len)); v[n]=1; for(k=n+1,#v, v[k]=(v[k-n]+v[k-m])%2); v=isperiodic(v); if(v,v,T(n,m,2*len+1))
%o a(n)=my(mx=T(n,1)); for(m=2,n-1,mx=max(T(n,m),mx)); mx
%Y Cf. A073726.
%K nonn
%O 2,1
%A _Charles R Greathouse IV_, Feb 28 2017
%E a(26)-a(34) from _Hiroaki Yamanouchi_, Apr 06 2017