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Search: id:A059347
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| A059347 |
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Difference array of Motzkin numbers A001006 read by antidiagonals. |
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+0
2
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| 1, 0, 1, 1, 1, 2, 0, 1, 2, 4, 2, 2, 3, 5, 9, 0, 2, 4, 7, 12, 21, 5, 5, 7, 11, 18, 30, 51, 0, 5, 10, 17, 28, 46, 76, 127, 14, 14, 19, 29, 46, 74, 120, 196, 323, 0, 14, 28, 47, 76, 122, 196, 316, 512, 835, 42, 42, 56, 84, 131, 207, 329, 525, 841, 1353, 2188, 0, 42, 84, 140, 224
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Row sums of odd rows (e.g. 4 = 1+1+2 for 3rd row) equal the Motzkin number of next row. Row sums of even rows equal the Motzkin number of the next row - n!/((n/2)!((n/2)+1)!) (i.e. A001006(n) - A000108(n/2) where A000108 are the Catalan numbers). - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Dec 05 2004
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REFERENCES
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F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 (1999) 73-112.
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EXAMPLE
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1; 0,1; 1,1,2; 0,1,2,4; ...
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CROSSREFS
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Top row is A001006, leading diagonals give A000108 (interspersed with 0's), A000108 doubled up, A059348.
Sequence in context: A166692 A046766 A003285 this_sequence A071496 A071502 A074704
Adjacent sequences: A059344 A059345 A059346 this_sequence A059348 A059349 A059350
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KEYWORD
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nonn,easy,nice,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 27 2001
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Feb 16 2001
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