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A106194 Triangle read by rows, generated from binomial transforms of odd numbers. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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: A212046 A232013 A246943 * A272099 A329033 A217234

Adjacent sequences:  A106191 A106192 A106193 * A106195 A106196 A106197

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Apr 24 2005

STATUS

approved

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Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)