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A140287
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Table T(n,k)= -2T(n-1,k)+T(n-1,k+1) = T(n,k-4), 0<=n.
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2
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0, 0, 1, -1, 0, 1, -3, 2, 1, -5, 8, -4, -7, 18, -20, 9, 32, -56, 49, -25, -120, 161, -123, 82, 401, -445, 328, -284, -1247, 1218, -940, 969, 3712, -3376, 2849, -3185, -10800, 9601, -8883, 10082, 31201, -28085, 27848, -30964, -90487, 84018, -86660, 93129, 264992, -254696
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OFFSET
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0,7
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COMMENTS
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The table is created from a nucleus (0,0,1,-1) in the upper row, periodic in each row with length 4 and extended downwards to further rows with the Pascal/Galton mixing coefficients (0,-2,1).
Each row may be regarded as coefficients in recurrences of a group of sequences, b_i(n)=sum_{k=1..4) T(i,k) b_i(n-k).
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LINKS
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FORMULA
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T(n,k) = T(n,k-1)+T(n,k-2)+T(n,k-3)+2T(n,k-4).
Row sums are sum_{k=1..4) T(n,k) = 0.
Row sums of absolute values: sum_{k=1..4} |T(n,k)| = A008776(n).
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EXAMPLE
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The table starts
0, 0, 1,-1, 0, 0, 1,-1,...
0, 1, -3, 2, 0, 1, -3, 2,...
1,-5, 8,-4, 1,-5, 8,-4,...
-7,18,-20, 9,-7,18,-20, 9,...
and only the first 4 columns (the non-redundant information) build the sequence.
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CROSSREFS
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KEYWORD
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sign,tabf,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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