A144024 Eigentriangle by rows, T(n,k) = A005614(n-k+1)*A144023(k-1).

1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 4, 1, 0, 1, 2, 0, 6, 0, 1, 0, 2, 4, 0, 10, 1, 0, 1, 0, 4, 6, 0, 17, 1, 1, 0, 20, 6, 10, 0, 29, 0, 1, 1, 0, 4, 0, 10, 17, 0, 4, 9, 1, 0, 1, 2, 0, 6, 0, 17, 29, 0, 82

Offset

1,10

Comments

Row sums = A144023, the INVERT transform of the rabbit sequence, A005614.

Left border = A005614.

Sum of n-th row terms = rightmost term of next row.

Links

Table of n, a(n) for n=1..66.

Formula

Eigentriangle by rows, T(n,k) = A005614(n-k+1)*A144023(k-1).

A005614 = the rabbit sequence, (1, 0, 1, 1, 0, 1, 0, 1,...)

A144023(k-1) = A144023 shifted to (1, 1, 1, 2, 4, 6, 10, 17, 29,...).

Example

First few rows of the triangle =
  1;
  0, 1;
  1, 0, 1;
  1, 1, 0, 2;
  0, 1, 1, 0, 4;
  1, 0, 1, 2, 0, 6;
  0, 1, 0, 2, 4, 0, 10;
  1, 0, 1, 0, 4, 6, 0, 17;
  1, 1, 0, 2, 0, 6, 10, 0, 29;
  ...;
Row 4 = (1, 1, 0, 2) = termwise product of (1, 1, 0, 1) and (1, 1, 1, 2); where (1, 1, 0, 1) = the first 4 terms of A005614 reversed. (1, 1, 1, 2) = the first 4 terms of shifted A144023.

Crossrefs

Cf. A005614, A144023.

Sequence in context: A236541 A113206 A158800 * A185249 A075107 A269953

Adjacent sequences: A144021 A144022 A144023 * A144025 A144026 A144027

Keyword

nonn,tabl,more

Author

Gary W. Adamson, Sep 07 2008

Status

approved