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Search: id:A058395
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| A058395 |
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A square array based on triangular numbers (A000217) with each term being the sum of 2 consecutive terms in the previous row. |
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+0
4
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| 1, 0, 1, 3, 1, 1, 0, 3, 2, 1, 6, 3, 4, 3, 1, 0, 6, 6, 6, 4, 1, 10, 6, 9, 10, 9, 5, 1, 0, 10, 12, 15, 16, 13, 6, 1, 15, 10, 16, 21, 25, 25, 18, 7, 1, 0, 15, 20, 28, 36, 41, 38, 24, 8, 1, 21, 15, 25, 36, 49, 61, 66, 56, 31, 9, 1, 0, 21, 30, 45, 64, 85, 102, 104, 80, 39, 10, 1, 28, 21, 36
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Changing the formula by replacing T(2n,0)=T(n,3) with T(2n,0)=T(n,m) for some other value of m would change the generating function to the coefficient of x^n in expansion of (1+x)^k/(1-x^2)^m. This would produce A058393, A058394, A057884 (and effectively A007318).
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FORMULA
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T(n, k)=T(n-1, k-1)+T(n, k-1) with T(0, k)=1, T(2n, 0)=T(n, 3) and T(2n+1, 0)=0. Coefficient of x^n in expansion of (1+x)^k/(1-x^2)^3.
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EXAMPLE
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Rows are (1,0,3,0,6,0,10,...), (1,1,3,3,6,6,...), (1,2,4,6,9,12,...), (1,3,6,10,15,21,...), (1,4,9,16,25,36,...) etc.
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CROSSREFS
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Rows are A000217 with zeros, A008805, A002620, A000217, A000290, A001844, A005899 etc. Columns are A000012, A001477, A016028 etc. Diagonals include A058396, A049611, A001793, A001788, A055580, A055581, A055582 etc. The triangle A055252 also appears in half of the array.
Sequence in context: A011354 A143119 A085565 this_sequence A035694 A006941 A076277
Adjacent sequences: A058392 A058393 A058394 this_sequence A058396 A058397 A058398
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Nov 24 2000
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