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Search: id:A004247
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| A004247 |
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Multiplication table read by antidiagonals: T(i,j) = ij (i>=0, j>=0). |
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+0
13
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| 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 4, 3, 0, 0, 4, 6, 6, 4, 0, 0, 5, 8, 9, 8, 5, 0, 0, 6, 10, 12, 12, 10, 6, 0, 0, 7, 12, 15, 16, 15, 12, 7, 0, 0, 8, 14, 18, 20, 20, 18, 14, 8, 0, 0, 9, 16, 21, 24, 25, 24, 21, 16, 9, 0, 0, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 0, 0, 11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11, 0, 0, 12, 22, 30, 36, 40, 42, 42, 40, 36, 30
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Table of xy, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...
Or, triangle read by rows, in which row n gives the numbers 0, n*1, (n-1)*2, (n-2)*3, ..., 2*(n-1), 1*n, 0.
Letting T(n,k) be the (k+1)st entry in the (n+1)st row (same numbering used for Pascal's triangle), T(n,k) is the dimension of the space of all k-dimensional subspaces of a (fixed) n-dimensional real vector space. - Paul Boddington (psb(AT)maths.warwick.ac.uk), Oct 21 2003
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LINKS
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T. D. Noe, Rows n=0..50 of triangle, flattened
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FORMULA
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a(n) = (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n) * (n-((trinv(n)*(trinv(n)-1))/2)); # A002262[ n ]*A025581[ n ] - Antti Karttunen
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EXAMPLE
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0; 0,0; 0,1,0; 0,2,2,0; 0,3,4,3,0; 0,4,6,6,4,0,; 0,5,8,9,8,5,0; ...
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MATHEMATICA
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Table[(x - y) y, {x, 0, 13}, {y, 0, x}] // Flatten (* Robert G. Wilson v (rgwv@rgwv.com), Oct 06 2007 *)
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CROSSREFS
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See A003991 for another version with many more comments.
Cf. A048720, A003056.
Sequence in context: A048720 A067138 A059692 this_sequence A014473 A101164 A062275
Adjacent sequences: A004244 A004245 A004246 this_sequence A004248 A004249 A004250
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KEYWORD
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tabl,nonn,easy,nice
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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Edited by njas, Sep 30 2007
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