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Search: id:A081422
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| A081422 |
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Triangle read by rows in which row n consists of the first n+1 n-gonal numbers. |
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+0
9
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| 1, 1, 1, 1, 2, 3, 1, 3, 6, 10, 1, 4, 9, 16, 25, 1, 5, 12, 22, 35, 51, 1, 6, 15, 28, 45, 66, 91, 1, 7, 18, 34, 55, 81, 112, 148, 1, 8, 21, 40, 65, 96, 133, 176, 225, 1, 9, 24, 46, 75, 111, 154, 204, 261, 325, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 1, 11, 30, 58, 95, 141
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Rows include A060354, A064808, A000600, A000603, A002411. Diagonals include A001093, A053698, A069778, A000578, A002414, A081423, A081435, A081436, A081437, A081438, A081441. Antidiagonals are composed of n-gonal numbers.
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LINKS
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T. D. Noe, Rows n=0..100 of triangle, flattened
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FORMULA
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Array of coefficients of x in the expansions of T(k, x)=(1+kx-(k-2)x^2)/(1-x)^4, k>-4.
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EXAMPLE
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The array starts
1 1 3 10 ...
1 2 6 16 ...
1 3 9 22 ...
1 4 12 28 ...
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CROSSREFS
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Sequence in context: A117938 A101912 A111808 this_sequence A027555 A059481 A113592
Adjacent sequences: A081419 A081420 A081421 this_sequence A081423 A081424 A081425
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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), Mar 21 2003
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