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Search: id:A097367
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| A097367 |
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Fibonacci regression array: For n>=2 and 1<=k<=n-1, T(n,k) is the last term before the first nonpositive term in the sequence n, k, n-k, 2k-n, 2n-3k, 5k-3n, ... |
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+0
3
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| 1, 2, 1, 3, 2, 2, 4, 3, 1, 3, 5, 4, 3, 2, 4, 6, 5, 4, 2, 3, 5, 7, 6, 5, 4, 1, 4, 6, 8, 7, 6, 5, 3, 3, 5, 7, 9, 8, 7, 6, 5, 2, 4, 6, 8, 10, 9, 8, 7, 6, 4, 2, 5, 7, 9, 11, 10, 9, 8, 7, 6, 3, 4, 6, 8, 10, 12, 11, 10, 9, 8, 7, 5, 1, 5, 7, 9, 11, 13, 12, 11, 10, 9, 8, 7, 4, 3, 6, 8, 10, 12, 14, 13, 12, 11
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OFFSET
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1,2
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FORMULA
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For n > k >= 1, define d(1)=n, d(2)=k, d(j) = d(j-2) - d(j-1) for j >= 3. Then d(j) = F(j-2)*n - F(j-1)*k for odd j>=1 and d(j) = F(j-1)*k - F(j-2)*n for even j>=2, where F(h)=A000045(h) = hth Fibonacci number. The sequence d is the aforementioned sequence n, k, n-k, 2k-n, 2n-3k, 5k-3n, ...
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EXAMPLE
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Rows 2,3,4,5,6:
1
2 1
3 2 2
4 3 1 3
5 4 3 2 4
T(8,5)=1, last term before 0 in 8,5,3,2,1,1,0,1,-1,...
T(8,6)=4, last term before -2 in 8,6,2,4,-2,6,-8,14,...
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CROSSREFS
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Cf. A000045, A097368, A097369.
Adjacent sequences: A097364 A097365 A097366 this_sequence A097368 A097369 A097370
Sequence in context: A069013 A029281 A126792 this_sequence A130211 A102364 A132923
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Aug 09 2004
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