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 A140056 Triangle of coefficients: f(x,y,n) = x^n - y^(n-1)*x - y^n; p(x,y,z,n) = f(x,y,n) + f(y,z,n) + f(z,x,n). 0
 -3, -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, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums are all -3. REFERENCES Weisstein, Eric W. "Klein Quartic." http://mathworld.wolfram.com/KleinQuartic.html LINKS Table of n, a(n) for n=1..57. FORMULA f(x,y,n)=x^n - y^(n - 1)*x - y^n; p(x,y,z,n)=f(x,y,n)+f(y,z,n)+f(z,x,n); EXAMPLE {-3}, {-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, 0, 0, -1}, {-1, -1, 0, 0, 0, 0, 0, 0, -1}, {-1, -1, 0, 0, 0, 0, 0, 0, 0, -1}. Polynomials before lower to x only are: -3, -x - y - z, -xy - x z - y z, -xy^2 - x^2 z - y z^2, -x y^3 - x^3 z - y z^3, -x y^4 - x^4 z - y z^4, ... MATHEMATICA f[x_, y_, n] = If[n > 0, x^n - y^(n - 1)*x - y^n, -1]; p[x_, y_, z_, n_] = f[x, y, n] + f[y, z, n] + f[z, x, n]; Table[ExpandAll[p[x, y, z, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, y, z, n] /. y -> 1 /. z -> 1, x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[p[x, y, z, n] /. y -> 1 /. z -> 1, x]], {n, 0, 10}]; CROSSREFS Sequence in context: A284993 A292068 A350942 * A240239 A247044 A083663 Adjacent sequences: A140053 A140054 A140055 * A140057 A140058 A140059 KEYWORD uned,tabl,sign AUTHOR Roger L. Bagula, Jun 14 2008 STATUS approved

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Last modified December 4 04:23 EST 2023. Contains 367541 sequences. (Running on oeis4.)