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 A143209 A "completed" set of cyclotomic polynomial with coefficients that are a triangular sequence: ( filled out with powers of (x+1)^m) p(x,n)=If[PrimeQ[n], Cyclotomic[n, x]*(x + 1), Cyclotomic[n, x]*(x + 1)^(n + 1 - Length[CoefficientList[Cyclotomic[n, x], x]])];. 0
 1, -1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 3, 3, 2, 3, 3, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 4, 6, 4, 2, 4, 6, 4, 1, 1, 3, 3, 2, 3, 3, 2, 3, 3, 1, 1, 5, 10, 10, 5, 2, 5, 10, 10, 5, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are: {1, 0, 4, 6, 8, 10, 16, 14, 32, 24, 64}. The problem with Cyclotomic polynomials is there uneven lengths: Here roots of -1 as (x+1) powers are used to fill out the triangle with positive coefficients. LINKS FORMULA p(x,n)=If[PrimeQ[n], Cyclotomic[n, x]*(x + 1), Cyclotomic[n, x]*(x + 1)^(n + 1 - Length[CoefficientList[Cyclotomic[n, x], x]])]; t(n,m)=Coefficients(p)x,n)) EXAMPLE {1}, {-1, 1}, {1, 2, 1}, {1, 2, 2, 1}, {1, 2, 2, 2, 1}, {1, 2, 2, 2, 2, 1}, {1, 3, 3, 2, 3, 3, 1}, {1, 2, 2, 2, 2, 2, 2, 1}, {1, 4, 6, 4, 2, 4, 6, 4, 1}, {1, 3, 3, 2, 3, 3, 2, 3, 3, 1}, {1, 5, 10, 10, 5, 2, 5, 10, 10, 5, 1} MATHEMATICA p[x_, n_] := If[PrimeQ[n], Cyclotomic[n, x]*(x + 1), Cyclotomic[n, x]*(x + 1)^(n + 1 - Length[CoefficientList[Cyclotomic[n, x], x]])]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A154325 A129765 A143187 * A163994 A156593 A206498 Adjacent sequences:  A143206 A143207 A143208 * A143210 A143211 A143212 KEYWORD uned,sign AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 20 2008 STATUS approved

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)