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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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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: A161094 A241597 A074807 * A002951 A093993 A193073

Adjacent sequences:  A165191 A165192 A165193 * A165195 A165196 A165197

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Sep 06 2009

STATUS

approved

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Last modified February 18 23:26 EST 2018. Contains 299330 sequences. (Running on oeis4.)