A130125 Triangle defined by A128174 * A130123, read by rows.

1, 0, 2, 1, 0, 4, 0, 2, 0, 8, 1, 0, 4, 0, 16, 0, 2, 0, 8, 0, 32, 1, 0, 4, 0, 16, 0, 64, 0, 2, 0, 8, 0, 32, 0, 128, 1, 0, 4, 0, 16, 0, 64, 0, 256, 0, 2, 0, 8, 0, 32, 0, 128, 0, 512, 1, 0, 4, 0, 16, 0, 64, 0, 256, 0, 1024, 0, 2, 0, 8, 0, 32, 0, 128, 0, 512, 0, 2048

Offset: 0

Author

Gary W. Adamson, May 11 2007

Keywords

• nonn
• tabl

Comments

Row sums = A000975: (1, 2, 5, 10, 21, 42, ...).

Examples

			First few rows of the triangle are:
  1;
  0, 2;
  1, 0, 4;
  0, 2, 0, 8;
  1, 0, 4, 0, 16;
  0, 2, 0, 8,  0, 32; ...
		

Links

• G. C. Greubel, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A000975, A128174, A130123.

Programs

GAP

Flat(List([0..10], n-> List([0..n], k-> 2^(k-1)*(1+(-1)^(n-k)) ))); # G. C. Greubel, Jun 05 2019

Magma

[[2^(k-1)*(1+(-1)^(n-k)): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Jun 05 2019

Mathematica

Table[2^(k-1)*(1+(-1)^(n-k)), {n,0,10}, {k,0,n}]//Flatten (* G. C. Greubel, Jun 05 2019 *)

PARI

{T(n,k) = 2^(k-1)*(1+(-1)^(n-k))}; \\ G. C. Greubel, Jun 05 2019

Sage

[[2^(k-1)*(1+(-1)^(n-k)) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Jun 05 2019

Formula

A128174 * A130123 as infinite lower triangular matrices. By columns, (2^k, 0, 2^k, 0, ...).

T(n,k) = 2^(k-1)*(1 + (-1)^(n-k)). - G. C. Greubel, Jun 05 2019

Extensions

More terms added by G. C. Greubel, Jun 05 2019