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Search: id:A080853
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| A080853 |
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Square array of generalized polygonal numbers, read by antidiagonals. |
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+0
8
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| 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 9, 7, 1, 1, 5, 16, 19, 11, 1, 1, 6, 25, 37, 33, 16, 1, 1, 7, 36, 61, 67, 51, 22, 1, 1, 8, 49, 91, 113, 106, 73, 29, 1, 1, 9, 64, 127, 171, 181, 154, 99, 37, 1, 1, 10, 81, 169, 241, 276, 265, 211, 129, 46, 1, 1, 11, 100, 217, 323, 391, 406, 365, 277
(list; table; graph; listen)
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OFFSET
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0,5
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FORMULA
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T(n, k)=C(k, 0)+C(k, 1)n+C(k, 2)n^2=(n^2*k^2-(n^2-2n)*k+2)/2 =(k(k-1)*n^2+2k*n+2)/2 Row n has g.f. (1+(n-2)x+(n^2-n+1)x^2)/(1-x)^3. Column k has g.f. (C(k-1, 0)+(C(k+1, 2)-2)*x+C(k-1, 2)*x^2)/(1-x)^3. Diagonals are given by (n^4+(2k-1)*n^3+((k-1)^2+1)*n^2+(1-(k-1)^2)*n+2)/2
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EXAMPLE
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Rows begin
1 1 1 1 1 ...
1 2 4 7 11 ...
1 3 9 19 33 ...
1 4 16 37 67 ...
1 5 25 61 113 ...
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CROSSREFS
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Rows include A000124, A058331, A080855, A080856, A080857, A080919.
Columns include A000290, A003215, A003215, A080859, A080860, A080861.
Sequence in context: A144042 A122084 A104559 this_sequence A071922 A138028 A009999
Adjacent sequences: A080850 A080851 A080852 this_sequence A080854 A080855 A080856
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 23 2003
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