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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

Table of n, a(n) for n=0..49.

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).

A140289(n)=T(n,1). A140290(n)=T(n,4).

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

Sequence in context: A209559 A081277 A079628 * A077951 A077976 A021912

Adjacent sequences:  A140284 A140285 A140286 * A140288 A140289 A140290

KEYWORD

sign,tabf,less

AUTHOR

Paul Curtz, May 24 2008

EXTENSIONS

Edited and extended by R. J. Mathar, Jul 22 2008

STATUS

approved

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Last modified February 17 17:12 EST 2019. Contains 320222 sequences. (Running on oeis4.)