cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A136673 Triangle of coefficients from a polynomial recursion for Galois field GF(2^n) polynomials: p(x,n)=(x+1)*p(x,n-1)-x*p(x,n-2); or f(x,n)=x^n+x+1;.

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%I A136673 #2 Mar 30 2012 17:34:25
%S A136673 2,1,1,2,1,1,1,1,1,0,1,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,
%T A136673 0,0,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1
%N A136673 Triangle of coefficients from a polynomial recursion for Galois field GF(2^n) polynomials: p(x,n)=(x+1)*p(x,n-1)-x*p(x,n-2); or f(x,n)=x^n+x+1;.
%C A136673 Row sums are:
%C A136673 {3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}
%C A136673 The result is very dependent on the two initial polynomials.
%D A136673 Taylor L. Booth, Sequential Machines and Automata Theory, John Wiley and Sons, Inc., 1967, Appendix I
%F A136673 p(x,0)=2+x;p(x,1)=1+2*x; p(x,n)=(x+1)*p(x,n-1)-x*p(x,n-2); or f(x,n)=x^n+x+1;
%e A136673 {2, 1},
%e A136673 {1, 2},
%e A136673 {1, 1, 1},
%e A136673 {1, 1, 0, 1},
%e A136673 {1, 1, 0, 0, 1},
%e A136673 {1, 1, 0, 0, 0, 1},
%e A136673 {1, 1, 0, 0, 0, 0, 1},
%e A136673 {1, 1, 0, 0, 0, 0, 0, 1},
%e A136673 {1, 1, 0, 0, 0, 0, 0, 0, 1},
%e A136673 {1, 1, 0, 0, 0, 0, 0, 0, 0, 1},
%e A136673 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1}
%t A136673 p[x, 0] = 2 + x; p[x, 1] = 1 + 2*x; p[x_, n_] := p[x, n] = (x + 1)*p[x, n - 1] - x*p[x, n - 2]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}] Flatten[a]
%Y A136673 Cf. A057764, A103204.
%K A136673 nonn,uned,tabl
%O A136673 1,1
%A A136673 _Roger L. Bagula_, Apr 05 2008