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A136266
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Coefficients of a new type of recursive polynomial based on Conway's A04001 chaotic sequence:B(x, n) = x*B(x, A004001(n - 1)) + B(x, n - A004001(n - 1))
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0
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1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 1, 0, 1, 3, 1, 0, 1, 3, 2, 0, 1, 3, 2, 1, 0, 1, 3, 3, 1, 0, 1, 4, 3, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 2, 0, 1, 4, 4, 2, 1, 0, 1, 4, 5, 2, 1, 0, 1, 4, 5, 3, 1, 0, 1, 4, 5, 4, 1, 0, 1, 4, 6, 4, 1, 0, 1, 5, 6, 4, 1, 0, 1, 5, 7, 4, 1, 0, 1, 5, 7, 5, 1, 0, 1, 5, 7, 5, 2
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OFFSET
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1,9
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COMMENTS
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Row sums are: {1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ...}
This sequence comes from trying to get a chaotic sequence like behavior in
a recursive polynomial. As far as I know this is a net type of triangular sequence
which I based on the similarity of the A049310
B(x,n)=x*B(x,n-1)+B(x,n-2)
to the Fibonacci sequence.
I use the Conway A004001 chaotic sequence to index this such that
I substitute:
n-1-> Conway[n - 1]
n-2-> n - Conway[n - 1]
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REFERENCES
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http://www-ec.njit.edu/~kappraff/
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LINKS
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Table of n, a(n) for n=1..100.
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FORMULA
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B(x, n) = x*B(x, A004001(n - 1)) + B(x, n - A004001(n - 1))
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EXAMPLE
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{1},
{0, 1},
{0, 1, 1},
{0, 1, 2},
{0, 1, 2, 1},
{0, 1, 3, 1},
{0, 1, 3, 2},
{0, 1, 3, 2, 1},
{0, 1, 3, 3, 1},
{0, 1, 4, 3, 1},
{0, 1, 4, 4, 1},
{0, 1, 4, 4, 2},
{0, 1, 4, 4, 2, 1},
{0, 1, 4, 5, 2, 1},
{0, 1, 4, 5, 3, 1},
{0, 1, 4, 5, 4, 1},
{0, 1, 4, 6, 4, 1},
{0, 1, 5, 6, 4, 1},
{0, 1, 5, 7, 4, 1},
{0, 1, 5, 7, 5, 1},
{0, 1, 5, 7, 5, 2}
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MATHEMATICA
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Clear[Conway] Conway[0] = 1; Conway[1] = 1; Conway[2] = 1; Conway[n_] := Conway[n] = Conway[Conway[n - 1]] + Conway[n - Conway[n - 1]]; Clear[B, x, n]; B[x, 0] = 1; B[x, 1] = x; B[x_, n_] := B[x, n] = x*B[x, Conway[n - 1]] + B[x, n - Conway[n - 1]]; Table[ExpandAll[B[x, n]], {n, 0, 10}]; a = Table[CoefficientList[B[x, n], x], {n, 0, 10}] Flatten[a]
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CROSSREFS
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Cf. A004001, A049310.
Sequence in context: A075993 A117170 A117466 * A054523 A161363 A106351
Adjacent sequences: A136263 A136264 A136265 * A136267 A136268 A136269
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KEYWORD
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nonn,uned,tabf
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AUTHOR
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Roger L. Bagula, Mar 18 2008
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STATUS
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approved
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