

A136266


Coefficients of a new type of recursive polynomial based on Conway's A004001 chaotic sequence: B(x, n) = x*B(x, A004001(n  1)) + B(x, n  A004001(n  1)).


0



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

1,9


COMMENTS

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,n1)+B(x,n2)
to the Fibonacci sequence.
I use the Conway A004001 chaotic sequence to index this such that
I substitute:
n1> Conway[n  1]
n2> n  Conway[n  1]


REFERENCES

http://wwwec.njit.edu/~kappraff/


LINKS

Table of n, a(n) for n=1..100.


FORMULA

B(x, n) = x*B(x, A004001(n  1)) + B(x, n  A004001(n  1)).


EXAMPLE

{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}


MATHEMATICA

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]


CROSSREFS

Cf. A004001, A049310.
Sequence in context: A075993 A117170 A117466 * A292047 A292049 A320341
Adjacent sequences: A136263 A136264 A136265 * A136267 A136268 A136269


KEYWORD

nonn,uned,tabf


AUTHOR

Roger L. Bagula, Mar 18 2008


STATUS

approved



