A136266 Expansion of B(x, n) = x*B(x, A004001(n - 1)) + B(x, n - A004001(n - 1)), irregular table read by rows.

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

Offset

1,9

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

Conway[0] = 1; Conway[1] = 1; Conway[2] = 1;
Conway[n_] := Conway[n] = Conway[Conway[n - 1]] + Conway[n - Conway[n - 1]];
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.

Sequence in context: A075993 A117170 A117466 * A292047 A292049 A320341

Adjacent sequences: A136263 A136264 A136265 * A136267 A136268 A136269

Keyword

nonn,uned,less,tabf

Author

Roger L. Bagula, Mar 18 2008

Status

approved