A106194 Triangle read by rows, generated from binomial transforms of odd numbers.

1, 4, 1, 12, 5, 1, 32, 17, 6, 1, 80, 49, 23, 7, 1, 192, 129, 72, 30, 8, 1, 448, 321, 201, 102, 38, 9, 1, 1024, 769, 522, 303, 140, 47, 10, 1, 2304, 1793, 1291, 825, 443, 187, 57, 11, 1, 5120, 4097, 3084, 2116, 1268, 630, 244, 68, 12, 1

Offset

0,2

Comments

Appending the binomial transform of the natural numbers, (A001792: 1, 3, 8, 20, 48...) to A106194 as a leftmost column creates triangle A055249.

Placing zeros into the offset spaces, column 1: 0, 1, 5, 17, 49...; is the binomial transform of 0, 1, 3, 5...; and alternatively the binomial transform of 0, 0, 1, 2, 3...

n-th column is the binomial transform of 1, 3, 5...prefaced by n zeros. n-th column is alternatively the binomial transform of 1, 2, 3...prefaced by (n+1) zeros. The triangle of A106194 is identical to the binomial transform (of natural numbers, prefaced with zeros) triangle: A055249, deleting the leftmost column.

Links

Table of n, a(n) for n=0..54.

Example

First few rows of the triangle are:
1;
4, 1;
12, 5, 1;
32, 17, 6, 1;
80, 49, 23, 7, 1;
192, 129, 72, 30, 8, 1;
448, 321, 201, 102, 38, 9, 1;
...

Crossrefs

Cf. A001792, A001787, A000337, A045618, A045889, A034009, A055250, A055249.

Sequence in context: A232013 A246943 A353791 * A272099 A329033 A217234

Adjacent sequences: A106191 A106192 A106193 * A106195 A106196 A106197

Keyword

nonn,tabl

Author

Gary W. Adamson, Apr 24 2005

Status

approved