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A165194
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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.
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3
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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
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OFFSET
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1,6
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COMMENTS
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Row sums = A000110, the Bell sequence starting with offset 1; (1, 2, 5, 15,...).
Rows tend to A165195.
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LINKS
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Table of n, a(n) for n=1..32.
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FORMULA
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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.
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EXAMPLE
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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).
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CROSSREFS
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A000110, A165195, A165196
Sequence in context: A331310 A241597 A074807 * A002951 A331287 A093993
Adjacent sequences: A165191 A165192 A165193 * A165195 A165196 A165197
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Sep 06 2009
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STATUS
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approved
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