A166555 Triangle read by rows, Sierpinski's gasket, A047999 * (1,2,4,8,...) diagonalized.

1, 1, 2, 1, 0, 4, 1, 2, 4, 8, 1, 0, 0, 0, 16, 1, 2, 0, 0, 16, 32, 1, 0, 4, 0, 16, 0, 64, 1, 2, 4, 8, 16, 32, 64, 128, 1, 0, 0, 0, 0, 0, 0, 0, 256, 1, 2, 0, 0, 0, 0, 0, 0, 256, 512, 1, 0, 4, 0, 0, 0, 0, 0, 256, 0, 1024

Offset

0,3

Comments

Row sums = A001317: (1, 3, 5, 15, 17, 51, 85,...).

Number of positive terms in n-th row (n>=0) equals to A000120(n). [From Vladimir Shevelev, Oct 25 2010]

Links

Table of n, a(n) for n=0..65.

Formula

Triangle read by rows, A047999 * Q. A047999 = Sierpinski's gasket, Q = an infinite lower triangular matrix with (1,2,4,8,...) as the main diagonal and the rest zeros.

Example

First few rows of the triangle =
1;
1, 2;
1, 0, 4;
1, 2, 4, 8;
1, 0, 0, 0, 16;
1, 2, 0, 0, 16,.32;
1, 0, 4, 0, 16,..0,..64;
1, 2, 4, 8, 16,.32,..64,..128;
1, 0, 0, 0,..0,..0,...0,....0,..256;
1, 2, 0, 0,..0,..0,...0,....0,..256,...512;
1, 0, 4, 0,..0,..0,...0,....0,..256,.....0,...1024;
1, 2, 4, 8,..0,..0,...0,....0,..256,...512,...l024,...2048;
1, 0, 0, 0, 16,..0,...0,....0,..256,.....0,......0,......0,..4096;
...

Crossrefs

Cf. A147999, A001317.

Sequence in context: A143724 A143425 A323376 * A136329 A122073 A106236

Adjacent sequences: A166552 A166553 A166554 * A166556 A166557 A166558

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 17 2009

Status

approved