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A101321
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Table T(n,m) = 1 + n*m*(m+1)/2 read by antidiagonals: centered polygonal numbers.
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26
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1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 7, 7, 4, 1, 1, 11, 13, 10, 5, 1, 1, 16, 21, 19, 13, 6, 1, 1, 22, 31, 31, 25, 16, 7, 1, 1, 29, 43, 46, 41, 31, 19, 8, 1, 1, 37, 57, 64, 61, 51, 37, 22, 9, 1, 1, 46, 73, 85, 85, 76, 61, 43, 25, 10, 1, 1, 56, 91, 109, 113, 106, 91, 71, 49, 28, 11, 1, 1, 67
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OFFSET
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0,5
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COMMENTS
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Row n gives the centered figurate numbers of the n-gon.
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LINKS
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FORMULA
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EXAMPLE
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The upper left corner of the infinite array T is
|0| 1 1 1 1 1 1 1 1 1 1 ... A000012
|1| 1 2 4 7 11 16 22 29 37 46 ... A000124
|2| 1 3 7 13 21 31 43 57 73 91 ... A002061
|3| 1 4 10 19 31 46 64 85 109 136 ... A005448
|4| 1 5 13 25 41 61 85 113 145 181 ... A001844
|5| 1 6 16 31 51 76 106 141 181 226 ... A005891
|6| 1 7 19 37 61 91 127 169 217 271 ... A003215
|7| 1 8 22 43 71 106 148 197 253 316 ... A069099
|8| 1 9 25 49 81 121 169 225 289 361 ... A016754
|9| 1 10 28 55 91 136 190 253 325 406 ... A060544
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MAPLE
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n*k*(k+1)/2+1 ;
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MATHEMATICA
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T[n_, m_] := 1 + n m (m + 1)/2;
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PROG
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(Iverson's J language) Let cfn be the formula above. Then the first 20 rows and columns of T are: T =: cfn / ~ i. 20 where i.
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CROSSREFS
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KEYWORD
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AUTHOR
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Eugene McDonnell (eemcd(AT)mac.com), Dec 24 2004
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EXTENSIONS
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STATUS
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approved
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