|
|
A140287
|
|
Table T(n,k)= -2T(n-1,k)+T(n-1,k+1) = T(n,k-4), 0<=n.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,7
|
|
COMMENTS
|
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).
|
|
LINKS
|
|
|
FORMULA
|
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).
|
|
EXAMPLE
|
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.
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,tabf,less
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|