Search: id:A157895
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%I A157895
%S A157895 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,
%T A157895 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,
%U A157895 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
%V A157895 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,
%W A157895 -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,
%X A157895 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
%N 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]]].
%C A157895 Row sums are:
%C A157895 {1, 2, 0, 6, 0, 0, 14, 18, 0, 0, 30, 0, 38, 42, 0, 0, 54, 0, 62, 0, 0,
               ...}.
%C A157895 This row sum minus one picks out as cyclotomic the primes; A002144:
%C A157895 {5,13,17,29,37,41,53,61,...}
%F A157895 p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2}];
%F A157895 q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2}];
%F A157895 t(x,n)=If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]];
%F A157895 out_(n,m)=coefficients(t(x,n)).
%e A157895 {1},
%e A157895 {1, 1},
%e A157895 {1, 1, -1, -1},
%e A157895 {1, 1, 1, 1, 1, 1},
%e A157895 {1, 1, 1, 1, -1, -1, -1, -1},
%e A157895 {1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1},
%e A157895 {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
%e A157895 {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
%e A157895 {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
%e A157895 {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 
               -1, -1, -1, -1},
%e A157895 {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}
%t A157895 Clear[p, q, t, x, n];
%t A157895 p[x_, n_] := Sum[x^i, {i, 0, (Prime[n] - 1)/2}];
%t A157895 q[x_, n_] := Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2}];
%t A157895 t[x_, n_] := If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]];
%t A157895 Table[ExpandAll[t[x, n]], {n, 0, 10}];
%t A157895 Table[CoefficientList[ExpandAll[t[x, n]], x], {n, 0, 10}];
%t A157895 Flatten[%]
%Y A157895 Sequence in context: A033999 A057077 A162511 this_sequence A063747 A077008 
               A158387
%Y A157895 Adjacent sequences: A157892 A157893 A157894 this_sequence A157896 A157897 
               A157898
%K A157895 sign,tabl,uned
%O A157895 0,1
%A A157895 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 08 2009

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