A174391 Triangle, read by row, of constant term of X^k modulo n-th cyclotomic polynomial.

1, 1, -1, 1, 0, -1, 1, 0, -1, 0, 1, 0, 0, 0, -1, 1, 0, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1

Offset: 1

Author

David A. Madore, Mar 18 2010

Keywords

• sign
• tabl

Comments

a(n,k) (for n>=1 and 0<=k

Examples

			For n=6, the 6th cyclotomic polynomial is Phi_6(X) = X^2-X+1, and the remainders of 1, X, X^2,..., X^5 mod Phi_6 are 1, X, X-1, -1, -X, -X+1, so a(6,k)=1,0,-1,-1,0,1 for k from 0 to 5. (This gives the terms 16 to 22 of this sequence.)
		

Programs

Sage

R. = QQ['x']; [[((x^k)%(R.cyclotomic_polynomial(n))).subs(0) for k in range(n)] for n in range(1,31)]

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