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A060964
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Table by antidiagonals where T(n,k)=n*T(n,k-1)-T(n,k-2) with T(n,0)=2 and T(n,1)=n.
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1
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2, 0, 2, -2, 1, 2, 0, -1, 2, 2, 2, -2, 2, 3, 2, 0, -1, 2, 7, 4, 2, -2, 1, 2, 18, 14, 5, 2, 0, 2, 2, 47, 52, 23, 6, 2, 2, 1, 2, 123, 194, 110, 34, 7, 2, 0, -1, 2, 322, 724, 527, 198, 47, 8, 2, -2, -2, 2, 843, 2702, 2525, 1154, 322, 62, 9, 2, 0, -1, 2, 2207, 10084, 12098, 6726, 2207, 488, 79, 10, 2, 2, 1, 2, 5778, 37634, 57965, 39202
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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FORMULA
| For all m, T(n, k) = T(n, |m|)*T(n, |k - m|) - T(n, |k - 2m|). T(n, 2k) = T(n, k)^2 - 2; T(n, 2k + 1) = T(n, k)*T(n, k + 1) - n. T(n, 3k) = T(n, k)^3 - 3*T(n, k); T(n, 4k) = T(n, k)^4 - 4*T(n, k)^2 + 2; T(n, 5k) = T(n, k)^5 - 5*T(n, k)^3 + 5*T(n, k) etc.
T(n, - k) = T(n, k); T( - n, k) = T( - n, - k) = T(n, k)*( - 1)^k. T(n, k) = {n*[{((n + sqrt(n^2 - 4))/2)^k} - {((n - sqrt(n^2 - 4))/2)^k} ] - 2*[{((n + sqrt(n^2 - 4))/2)^(k - 1)} - {((n - sqrt(n^2 - 4))/2)^(k - 1)} ]}/[sqrt(n^2 - 4) ].
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EXAMPLE
| Rows start (2, 0, -2, 0, 2, 0, -2,...), (2, 1, -1, -2, -1, 1, 2,...), 2, 2, 2, 2, 2, 2, 2,...), (2, 3, 7, 18, 47, 123, 322,...), (2, 4, 14, 52, 194, 724, 2702,...), ...
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CROSSREFS
| Rows include A057079, A007395, A005248, A003500, A003501, A003499, A056854, A056918. Columns include A007395, A001477, A008865, A058794.
Sequence in context: A061895 A129678 A023604 * A118206 A029314 A071635
Adjacent sequences: A060961 A060962 A060963 * A060965 A060966 A060967
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KEYWORD
| sign,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), May 09 2001
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