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Search: id:A144025
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| 1, 1, 1, 2, 1, 2, 4, 2, 2, 5, 9, 4, 4, 5, 13, 21, 9, 8, 10, 13, 35, 51, 21, 18, 20, 26, 35, 96, 127, 51, 42, 45, 52, 70, 96, 267, 323, 127, 102, 105, 117, 140, 192, 267, 750, 835, 323, 254, 255, 273, 315, 384, 534, 720, 2123, 2188, 835, 646, 635, 663, 735, 864, 1068
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OFFSET
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0,4
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COMMENT
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Left border = Motzkin numbers, A001006.
Right border = A005773.
Row sums = A005773 shifted: (1, 2, 5, 13, 35, 96, 267,...).
Sum of n-th row terms = rightmost term of next row.
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FORMULA
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Eigentriangle by rows, A001006(n-k)*A005773(k); 0<=k<=n
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EXAMPLE
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First few rows of the triangle =
1;
1, 1;
2, 1, 2;
4, 2, 2, 5;
9, 4, 4, 5, 13;
21, 9, 8, 10, 13, 35;
51, 21, 18, 20, 26, 35, 96;
127, 51, 42, 45, 52, 70, 96, 267;
323, 127, 102, 105, 117, 140, 192, 267, 750;
835, 323, 254, 255, 273, 315, 384, 534, 720, 2123;
...
Row 3 = (4, 2, 2, 5) = termwise product of (4, 2, 1, 1) and the first 4 terms of A005773: (1, 1, 2, 5) = (4*1, 2*1, 1*2, 1*5). (4, 2, 1, 1) = the first 4 terms of A001066, reversed.
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CROSSREFS
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A001066, Cf. A005773
Sequence in context: A145173 A082793 A114929 this_sequence A058573 A117268 A119538
Adjacent sequences: A144022 A144023 A144024 this_sequence A144026 A144027 A144028
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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 07 2008
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