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A193650 Q-residue of the coefficient triangle (A076699) of the cyclotomic polynomials, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.) 2

%I #5 Mar 30 2012 18:57:38

%S 1,0,3,7,10,31,24,127,136,292,352,2047,1664,8191,5504,9664,32896,

%T 131071,116736,524287,419840,603904,1398784,8388607,7897088,17318416

%N Q-residue of the coefficient triangle (A076699) of the cyclotomic polynomials, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.)

%C For the definition of Q-residue, see A193649.

%t q[n_, k_] := 1;

%t r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}]

%t p[n_, k_] := Coefficient[Cyclotomic[n, x], x, k]

%t v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]

%t Table[v[n], {n, 0, 25}] (* A193650 *)

%t TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]

%t Table[r[k], {k, 0, 8}] (* 2^k *)

%t TableForm[Table[p[n, k], {n, 0, 8}, {k, 0, n}]] (* A076699 *)

%Y Cf. A193649, A076699.

%K nonn

%O 0,3

%A _Clark Kimberling_, Aug 02 2011

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Last modified August 21 13:43 EDT 2024. Contains 375353 sequences. (Running on oeis4.)