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Search: id:A144961
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| A144961 |
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Eigentriangle, left border = Padovan sequence, right border and row sums = modified Fibonacci sequences. |
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1
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| 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 3, 1, 1, 0, 1, 0, 0, 5, 1, 1, 1, 0, 2, 0, 0, 8, 2, 1, 1, 1, 0, 3, 0, 0, 13, 2, 2, 1, 1, 2, 0, 5, 0, 0, 21, 3, 2, 2, 1, 2, 3, 0, 8, 0, 0, 34, 4, 3, 2, 2, 2, 3, 5, 0, 13, 0, 0, 55
(list; table; graph; listen)
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OFFSET
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0,15
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COMMENT
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Left border = A000931, the Padovan sequence: (1, 0, 0, 1, 0, 1, 1, 1, 2, 2,...).
Right border = (1, 1, 1, 1, 2, 3, 5, 8, 13, 21,...)
Row sums = (1, 1, 1, 2, 3, 5, 8, 13, 21, 34,...).
Sum of n-th row terms = rightmost term in next row.
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FORMULA
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Triangle read by rows, termwise products of a Padovan "decrescendo" triangle: (1; 0,1; 0,0,1; 1,0,0,1,...) and the Fibonacci series preceded by two 1's: (1, 1, 1, 1, 2, 3, 5, 8,...); (i.e. the INVERT transform of the Padovan sequence).
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EXAMPLE
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First few rows of the triangle =
1;
0, 1;
0, 0, 1;
1, 0, 0, 1;
0, 1, 0, 0, 2;
1, 0, 1, 0, 0, 3;
1, 1, 0, 1, 0, 0, 5;
1, 1, 1, 0, 2, 0, 0, 8;
2, 1, 1, 1, 0, 3, 0, 0, 13;
2, 2, 1, 1, 2, 0, 5, 0, 0, 21;
3, 2, 2, 1, 2, 3, 0, 8, 0, 0, 34;
4, 3, 2, 2, 2, 3, 50, 13, 0, 0, 55;
...
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CROSSREFS
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A000931
Sequence in context: A116488 A145765 A157424 this_sequence A144627 A135929 A080733
Adjacent sequences: A144958 A144959 A144960 this_sequence A144962 A144963 A144964
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 27 2008
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