1,17

Row sums are;

{1, 1, 1, 0, 2, -3, 3, 1, -3, 1, 3};

The new polynomials that result should be "Field -Like"

as well as they are representation of the quotient group of the type;

GF(2^Prime[n])/Cyclotomic(Prime[n])

Galois polynomial GF(2^p) g[x,p]=x^p+x+1 Cyclotomic polynomial for primes: c[x,p]=Sum[x^i,{i,0,p}] ratio polynomial: q[x,p]=c[x,p]/g[x,p] Toral inverse for expansion: p[x,p]=x^p*g[1/x,p]/(x^p*c[x,p]) a(n,m)=Anti-diagonal Coefficients(p[x,p]).

{{1},

{0, 1},

{1, -1, 1},

{-1, 1, -1, 1},

{1, 1, 0, -1, 1},

{-1, -2, 0, 0, -1, 1},

{1, 1, 1, 0, 0, -1, 1},

{-1, 1, 1, 0, 0, 0, -1, 1},

{1, -2, -2, 0, 0, 0, 0, -1, 1},

{-1, 1, 0, 1, 0, 0, 0, 0, -1, 1},

{1, 1, 0, 1, 0, 0, 0, 0, 0, -1, 1}}

p[x_, n_] = (x^Prime[n] + x^(Prime[n] - 1) + 1)/Cyclotomic[Prime[n], x] a = Table[CoefficientList[Normal[Series[p[x, n], {x, 0, 30}]], x], {n, 1, 31}]; (* anti-diagonal triangular sequence representation*) b = Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 11}]; Flatten[b]

Sequence in context: A060952 A037844 A037880 this_sequence A124764 A151899 A079632

Adjacent sequences: A140695 A140696 A140697 this_sequence A140699 A140700 A140701

uned,tabl,sign

Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 11 2008