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%I #3 Oct 12 2012 14:54:55
%S 0,0,1,0,1,1,-3,1,1,5,-5,1,1,7,13,-8,1,1,10,19,29,-13,1,1,15,29,57,86,
%T -21,1,1,23,45,89,155,244,-34,1,1,36,71,141,246,421,667,-55,1,1,57,
%U 113,225,393,673,1121,1794
%N A triangle sequence of determinants: a(n)=A000045(n); t(n,m)=a(m)*(a(n) + 1) - If[ m < n, Round[(a(m) - 1)/a(n) + 1], a(n) + 1]*a(n).
%C Row sums are:{0, 1, 2, 4, 17, 52, 176, 537, 1550, 4323}.
%F a(n)=A000045(n)+1;b(n)=A000045(n+1)-1; t(n,m)=a(m)*(a(n) + 1) - If[ m < n, Round[(a(m) - 1)/a(n) + 1], a(n) + 1]*a(n).
%e {0},
%e {0, 1},
%e {0, 1, 1},
%e {-3, 1, 1, 5},
%e {-5, 1, 1, 7, 13},
%e {-8, 1, 1, 10, 19, 29},
%e {-13, 1, 1, 15, 29, 57, 86},
%e {-21,1, 1, 23, 45, 89, 155, 244},
%e {-34, 1, 1, 36, 71, 141, 246, 421, 667},
%e {-55, 1, 1, 57, 113, 225, 393, 673, 1121, 1794}
%t Clear[a, b, t, n, m] a[n_] := Fibonacci[n] + 1; t[n_, m_] := a[m]*(a[n] + 1) - If[ m < n, Round[(a[m] - 1)/a[n] + 1], a[n] + 1]*a[n]; Table[Table[t[n, m], {m, 0, n - 1}], {n, 1, 10}]; Flatten[%]
%Y Cf. A000045.
%K uned,sign
%O 1,7
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 08 2008
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