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.
%I A174391 #8 Mar 12 2015 23:33:01 %S A174391 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, %T A174391 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, %U A174391 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 %N A174391 Triangle, read by row, of constant term of X^k modulo n-th cyclotomic polynomial. %C A174391 a(n,k) (for n>=1 and 0<=k<n) is the constant term in the polynomial remainder of X^k modulo the n-th cyclotomic polynomial; this sequence reads the triangle a(n,k) by rows (a(1,0)=1, a(2,0)=1, a(2,1)=-1, a(3,0)=1, a(3,1)=0, a(3,2)=-1, etc.). For each n, the finite sequence a(n,k), seen as a cyclic sequence of length n, has the property that the sum of every d'th term, for d dividing n, is zero, starting anywhere. %e A174391 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.) %o A174391 (Sage) R.<x> = QQ['x']; [[((x^k)%(R.cyclotomic_polynomial(n))).subs(0) for k in range(n)] for n in range(1,31)] %K A174391 sign,tabl %O A174391 1,1 %A A174391 _David A. Madore_, Mar 18 2010