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Search: id:A085740
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| A085740 |
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T(n)^2-n^2, where T(n) is a triangular number. |
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+0
1
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| 0, 0, 5, 27, 84, 200, 405, 735, 1232, 1944, 2925, 4235, 5940, 8112, 10829, 14175, 18240, 23120, 28917, 35739, 43700, 52920, 63525, 75647, 89424, 105000, 122525, 142155, 164052, 188384, 215325, 245055, 277760, 313632, 352869, 395675, 442260
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=A000096(n)*A000217(n-1).
a(n) is the dimension of the second Cartan power of sl(n, C), which is the irreducible representation of sl(n, C) the highest weight of which is twice that of the adjoint representation. - Daniel Fox (fox(AT)math.gatech.edu), Jan 01, 2006.
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FORMULA
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n^2*(n^2+2n-3)/4
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EXAMPLE
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a(3)=T(3)^2-3^2=6^2-9=36-9=27
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PROGRAM
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(PARI) for(n=0, 50, print1(n^2*(n^2-9)/4", "))
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CROSSREFS
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Cf. A000096, A000217.
Sequence in context: A137117 A064675 A135713 this_sequence A129868 A069993 A009027
Adjacent sequences: A085737 A085738 A085739 this_sequence A085741 A085742 A085743
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Jul 21 2003
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