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Search: id:A101321
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| A101321 |
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Table T(n,m) = 1+n*m*(m+1)/2 read by anti-diagonals. |
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3
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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
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row n gives the centered figurate numbers of the n-gon.
Anti-diagonal sums are in A101338.
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FORMULA
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T(n,2) = A016777(n). T(n,3)=A016921(n). T(n,4)=A017281(n).
T(10,m) = A062786(m+1).
T(11,m) = A069125(m+1).
T(12,m) = A003154(m+1).
T(13,m) = A069126(m+1).
T(14,m) = A069127(m+1).
T(15,m) = A069128(m+1).
T(16,m) = A069129(m+1).
T(17,m) = A069130(m+1).
T(18,m) = A069131(m+1).
T(19,m) = A069132(m+1).
T(20,m) = A069133(m+1).
n-th row of the array = A001263 * [1, n, 0, 0, 0,...]. E.g. A001263 * [1, 2, 0, 0, 0,...] = (1, 3, 7, 13, 21, 31, 43,...) - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 30 2007
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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
T(5,11) is 331 because we can write 1+5*(11+11^2)/2, or 1+5*66, or 331.
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PROGRAM
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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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Cf. A001263.
Sequence in context: A034367 A058717 A034371 this_sequence A091186 A138155 A055587
Adjacent sequences: A101318 A101319 A101320 this_sequence A101322 A101323 A101324
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KEYWORD
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easy,nonn,tabl
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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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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 21 2009
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