A165194 Triangle of 2^n terms by rows, left half of (n+1)-th row = row n; right half = "reverse and increment" row n; using terms in A000110.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 5, 2, 1, 1, 1, 2, 1, 2, 5, 2, 1, 1, 2, 5, 15, 5, 2, 5, 2, 1

Offset

1,6

Comments

Row sums = A000110, the Bell sequence starting with offset 1; (1, 2, 5, 15,...).

Rows tend to A165195.

Links

Table of n, a(n) for n=1..32.

Formula

Given the Bell sequence, A000110: (1, 1, 2, 5, 15,...); row 1 = 1, row 2 =

(1, 1);...where left half of row (n+1) = row n. Right half of row (n+1)

= reversal of row n, replacing terms with the next Bell number.

Example

First few rows of the triangle =
1;
1, 1;
1, 1, 2, 1;
1, 1, 2, 1, 2, 5, 2, 1;
1, 1, 2, 1, 2, 5, 2, 1, 2, 5, 15, 5, 2, 5, 2, 1;
...
For example: row 4, left half = (1, 1, 2, 1); right half = (1, 2, 1, 1)
replaced with the next higher Bell numbers: (2, 5, 2, 1). Appending the two \kQ halves, we obtain row 4: (1, 1, 2, 1, 2, 5, 2, 1), sum = 15 = A000110(4).

Crossrefs

A000110, A165195, A165196

Sequence in context: A241597 A374164 A074807 * A002951 A331287 A365105

Adjacent sequences: A165191 A165192 A165193 * A165195 A165196 A165197

Keyword

nonn,tabf

Author

Gary W. Adamson, Sep 06 2009

Status

approved