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Search: id:A135997
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| A135997 |
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Table of triplets T(k,m)= k (m=1), 2-k (m=2) and 1-k (m=3). |
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+0
2
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| 0, 2, 1, 1, 1, 0, 2, 0, -1, 3, -1, -2, 4, -2, -3, 5, -3, -4, 6, -4, -5, 7, -5, -6, 8, -6, -7, 9, -7, -8, 10, -8, -9, 11, -9, -10, 12, -10, -11, 13, -11, -12, 14, -12, -13, 15, -13, -14, 16, -14, -15, 17, -15, -16, 18, -16, -17, 19, -17, -18, 20, -18, -19, 21, -19, -20, 22, -20, -21, 23
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The table comprises recurrence coefficients for Fibonacci-related sequences b_k(n)=sum_{m=1..3} T(k,m)*b_k(n-m). The first row coefficients (0,2,1) are used in A008346, b(n)=2b(n-2)+b(n-3), for example. The 2nd row coefficients (1,1,0) represent b(n)=b(n-1)+b(n-2) of A000045, for example.
The 3rd row coefficients (2,0,-1) are used in A001611, A020706 and Pisot sequences like A018910.
The 4th row coefficients (3,-1,-2) are used in A052550, A052911, A074878 or A088859, for example.
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FORMULA
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Row sums: sum_{m=1..3} T(k,m) = A022959(k).
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EXAMPLE
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The table has 3 columns and starts
0, 2, 1;
1, 1, 0;
2, 0,-1;
3,-1,-2;
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CROSSREFS
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Sequence in context: A117274 A140883 A064744 this_sequence A026609 A090340 A117162
Adjacent sequences: A135994 A135995 A135996 this_sequence A135998 A135999 A136000
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KEYWORD
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sign,tabf,less,easy
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Mar 03 2008
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EXTENSIONS
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Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 22 2008
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