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Search: id:A108283
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| A108283 |
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Triangle read by rows, generated from (...3, 2, 1). |
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+0
3
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| 1, 1, 3, 1, 5, 6, 1, 7, 17, 10, 1, 9, 34, 49, 15, 1, 11, 57, 142, 129, 21, 1, 13, 86, 313, 547, 321, 28, 1, 15, 121, 586, 1593, 2005, 769, 36
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Inverse binomial transforms of each column form the rows of A108284. Rightmost diagonal = triangular numbers, (A000217); while diagonals going to the left from (1, 3, 6...) are A000337 starting with 1: (1, 5, 17, 49...); A014915: (1, 7, 34, 142...); A014916: (1, 9, 57...); A014917: (1, 11, 86...). The first few rows of the triangle are: 1; 1, 3; 1, 5, 6; 1, 7, 17, 10; 1, 9, 34, 49, 15; 1, 11, 57, 142, 129, 21; ...
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FORMULA
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n-th column = f(x), x = 1, 2, 3; n*x^(n-1) + (n-1)*x^(n-2) + (n-3)*x^(n-3) + ...+ 1.
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EXAMPLE
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4-th column = 10, 49, 142, 313... = f(x), x = 1, 2, 3; 4x^3 + 3x^2 + 2x + 1. f(3) = 142.
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CROSSREFS
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Cf. A108284, A000217, A000337, A014915, A014916, A014917.
Sequence in context: A089028 A134083 A113445 this_sequence A016600 A130418 A038871
Adjacent sequences: A108280 A108281 A108282 this_sequence A108284 A108285 A108286
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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 30 2005
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