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

0,3

Comments

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

Links

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

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

Example

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; ...

Mathematica

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

Prog

(PARI) {T(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
(Sage) [[2^(k-1)*(1+(-1)^(n-k)) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Jun 05 2019
(GAP) Flat(List([0..10], n-> List([0..n], k-> 2^(k-1)*(1+(-1)^(n-k)) ))); # G. C. Greubel, Jun 05 2019

Crossrefs

Cf. A000975, A128174, A130123.

Sequence in context: A363032 A185964 A143424 * A336517 A317552 A214809

Adjacent sequences: A130122 A130123 A130124 * A130126 A130127 A130128

Keyword

nonn,tabl

Author

Gary W. Adamson, May 11 2007

Extensions

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

Status

approved