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A014430
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Subtract 1 from Pascal's triangle, read by rows.
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5
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1, 2, 2, 3, 5, 3, 4, 9, 9, 4, 5, 14, 19, 14, 5, 6, 20, 34, 34, 20, 6, 7, 27, 55, 69, 55, 27, 7, 8, 35, 83, 125, 125, 83, 35, 8, 9, 44, 119, 209, 251, 209, 119, 44, 9, 10, 54, 164, 329, 461, 461, 329, 164, 54, 10, 11, 65, 219, 494, 791, 923, 791, 494, 219, 65, 11
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Each value of the sequence (T(x,y)) is equal to the sum of all values in Pascal's Triangle that are in the rectangle defined by the tip (0,0) and the position (x,y). - Florian Kleedorfer (florian.kleedorfer(AT)austria.fm), May 23 2005
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FORMULA
| T(n, k) = T(n-1, k) + T(n-1, k-1) + 1, T(0, 0)=1. - R. Stephan, Jan 23 2005
G.f.: 1 / [(1-x)*(1-xy)*(1-x(1+y)) ]. - R. Stephan, Jan 24 2005
Generating function: T(N, K)=sum(k=0...K){sum(n=k...k+(N-K)){C(n, k)}}. - Florian Kleedorfer (florian.kleedorfer(AT)austria.fm), May 23 2005
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EXAMPLE
| 1; 2 2; 3 5 3; 4 9 9 4; ...
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CROSSREFS
| Cf. A007318.
Triangle with zeros: A014473.
Sequence in context: A129312 A115262 A128141 * A196436 A197199 A196957
Adjacent sequences: A014427 A014428 A014429 * A014431 A014432 A014433
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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