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A013596
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Irregular triangle of coefficients of cyclotomic polynomial Phi_n(x) (exponents in decreasing order).
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12
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1, 0, 1, -1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 0, 1, -1, 1, 0, -1, 1, 1, 0, 0, 0, 0
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OFFSET
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0,3440
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COMMENTS
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We follow Maple in defining Phi_0 to be x; it could equally well be taken to be 1.
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REFERENCES
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E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, 1968; see p. 90.
Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, p. 325.
K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer, 1982, p. 194.
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LINKS
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EXAMPLE
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Phi_0 = x --> Row 0: [1, 0]
Phi_1 = x - 1 --> Row 1: [1, -1]
Phi_2 = x + 1 --> Row 2: [1, 1]
Phi_3 = x^2 + x + 1 --> Row 3: [1, 1, 1]
Phi_4 = x^2 + 1 --> Row 4: [1, 0, 1]
etc. After row zero, each row n has A039649(n) terms.
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MAPLE
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with(numtheory): [ seq(cyclotomic(n, x), n=0..48) ];
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MATHEMATICA
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Join[{1, 0}, Table[ CoefficientList[ Cyclotomic[n, x], x] // Reverse, {n, 1, 16}] // Flatten] (* Jean-François Alcover, Dec 11 2012 *)
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PROG
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(PARI)
A013595row(n) = { if(!n, p=x, p = polcyclo(n)); Vecrev(p); }; \\ This function from Michel Marcus's code for A013595.
n=0; for(r=0, 385, v=A013595row(r); k=length(v); while(k>0, write("b013596.txt", n, " ", v[k]); n=n+1; k=k-1)); \\ Antti Karttunen, Aug 13 2017
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CROSSREFS
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Version with reversed rows: A013595.
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KEYWORD
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sign,easy,nice,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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