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Search: id:A106396
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| A106396 |
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Triangle read by rows, generated from the Narayana triangle as a matrix. |
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+0
1
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| 1, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 7, 5, 2, 1, 1, 11, 13, 5, 2, 1, 1, 16, 31, 14, 5, 2, 1, 1, 22, 66, 41, 14, 5, 2, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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The n-th column starting from the top has the first n terms in the Catalan sequence: (1, 2, 5, 14...)
First few rows of the triangle are:
1;
1, 1;
1, 2, 1;
1, 4, 2, 1;
1, 7, 5, 2, 1;
1, 11, 13, 5, 2, 1;
1, 16, 31, 14, 5, 2, 1;
...
Second column = A000124.
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FORMULA
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n-th column (offset) is generated by P * V; P = the Narayana triangle as an infinite lower triangular matrix, V = vector for n-th column comprised of n leading 1's and the rest zeros (e.g. V for 3rd column = [1, 1, 1, 0, 0, 0...].
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EXAMPLE
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Col. 2 offset = 1, 2, 4, 7, 11, 16, 22...since P * [1, 1, 0, 0, 0...] = 1, 2, 4, 7, 11...
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CROSSREFS
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Cf. A000124, A001263.
Sequence in context: A092479 A124022 A098063 this_sequence A140998 A048004 A114394
Adjacent sequences: A106393 A106394 A106395 this_sequence A106397 A106398 A106399
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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), May 01 2005
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