|
Search: id:A157895
|
|
|
| A157895 |
|
Coefficients of polynomials of a prime like factor set : p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2}]; q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2}]; t(x,n)=If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]]. |
|
+0
1
|
|
| 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; table; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
Row sums are:
{1, 2, 0, 6, 0, 0, 14, 18, 0, 0, 30, 0, 38, 42, 0, 0, 54, 0, 62, 0, 0,...}.
This row sum minus one picks out as cyclotomic the primes; A002144:
{5,13,17,29,37,41,53,61,...}
|
|
FORMULA
|
p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2}];
q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2}];
t(x,n)=If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]];
out_(n,m)=coefficients(t(x,n)).
|
|
EXAMPLE
|
{1},
{1, 1},
{1, 1, -1, -1},
{1, 1, 1, 1, 1, 1},
{1, 1, 1, 1, -1, -1, -1, -1},
{1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1},
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
|
|
MATHEMATICA
|
Clear[p, q, t, x, n];
p[x_, n_] := Sum[x^i, {i, 0, (Prime[n] - 1)/2}];
q[x_, n_] := Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2}];
t[x_, n_] := If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]];
Table[ExpandAll[t[x, n]], {n, 0, 10}];
Table[CoefficientList[ExpandAll[t[x, n]], x], {n, 0, 10}];
Flatten[%]
|
|
CROSSREFS
|
Sequence in context: A033999 A057077 A162511 this_sequence A063747 A077008 A158387
Adjacent sequences: A157892 A157893 A157894 this_sequence A157896 A157897 A157898
|
|
KEYWORD
|
sign,tabl,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 08 2009
|
|
|
Search completed in 0.002 seconds
|
