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 A060964 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. 1

%I

%S 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,

%T 47,52,23,6,2,2,1,2,123,194,110,34,7,2,0,-1,2,322,724,527,198,47,8,2,

%U -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

%N 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.

%F 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.

%F 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) ].

%e 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,...), ...

%Y Rows include A057079, A007395, A005248, A003500, A003501, A003499, A056854, A056918. Columns include A007395, A001477, A008865, A058794.

%K sign,tabl

%O 0,1

%A _Henry Bottomley_, May 09 2001

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Last modified December 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.)