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Search: id:A142709
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| A142709 |
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Polynomials made from cycloidal standing waves: p(x,n)=(4*n + 2)*x + x^n. |
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+0
1
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| 1, 2, 0, 7, 0, 10, 1, 0, 14, 0, 1, 0, 18, 0, 0, 1, 0, 22, 0, 0, 0, 1, 0, 26, 0, 0, 0, 0, 1, 0, 30, 0, 0, 0, 0, 0, 1, 0, 34, 0, 0, 0, 0, 0, 0, 1, 0, 38, 0, 0, 0, 0, 0, 0, 0, 1, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are:
{3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43};
The cycloid graphic parametrics are:
fc(t,n)=(2-1/n)*Cos[t]/2+Cos[(n-1)*t]/2*n;
fs(t,n)=(2-1/n)*Sin[t]/2+Sin[(n-1)*t]/2*n;
fe(t,n)=(2-1/n)*Exp[I*t]/2+Exp[I*(n-1)*t]/2*n;
Substitutions of x->Exp[i*x] and m->n-1
and multiplication by 2*n give the polynomials.
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FORMULA
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p(x,n)=(4*n + 2)*x + x^n; t(n,m)=Coefficients)p(x,n)).
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EXAMPLE
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{1, 2},
{0, 7},
{0, 10, 1},
{0, 14, 0, 1},
{0, 18, 0, 0, 1},
{0, 22, 0, 0, 0, 1},
{0, 26, 0, 0, 0, 0, 1},
{0, 30, 0, 0, 0, 0, 0, 1},
{0, 34, 0, 0, 0, 0, 0, 0, 1},
{0, 38, 0, 0, 0, 0, 0, 0, 0, 1},
{0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 1}
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MATHEMATICA
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Clear[p, x, n, m] p[x_, n_] = (4*n + 2)*x + x^n; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A079203 A151751 A021487 this_sequence A022897 A156442 A140663
Adjacent sequences: A142706 A142707 A142708 this_sequence A142710 A142711 A142712
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 25 2008
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