

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...
nth column is the binomial transform of 1, 3, 5...prefaced by n zeros. nth 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



