A140287 Table T(n,k) = -2*T(n-1,k)+T(n-1,k+1) = T(n,k-4), 0<=n.

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

Offset: 0

Author

Paul Curtz, May 24 2008

Keywords

• sign
• tabf
• less

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).

Examples

			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.
		

Formula

T(n,k) = T(n,k-1)+T(n,k-2)+T(n,k-3)+2*T(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).

Extensions

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