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

Author

Roger L. Bagula, Mar 18 2008

Keywords

• nonn
• uned
• less
• tabf

Examples

			{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}
		

Crossrefs

Cf. A004001.

Programs

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]

Formula

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