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Search: id:A136266
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| A136266 |
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Kappraff polynomials: 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)): (I'm naming these Kappraff polynomials for the inspiration that Jay Kappraff has had in the area of sequence research over the years. Without him and Gary Adamson, nothing would have been done by me in this area. ). |
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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
(list; graph; listen)
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OFFSET
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1,9
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COMMENT
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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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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 this_sequence A054523 A106351 A096800
Adjacent sequences: A136263 A136264 A136265 this_sequence 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 (rlbagulatftn(AT)yahoo.com), Mar 18 2008
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