OFFSET
1,9
FORMULA
Formula: (C_n)ij = Sum(k=0..j, (-1)^k * C(j, k) * C(n-j, i-k)).
Recurrence: (C_n)i,j = (C_(n-1))i,j + (C_(n-1))i-1,j for all j < n; (C_n)i,j = (C_(n-1))i,j-1 - (C_(n-1))i-1,j-1 for all j > 0.
EXAMPLE
C_0 = [1]
C_1 = [1 1 / 1 -1]
C_2 is equal to:
|1 1 1|
|2 0 -2|
|1 -1 1|
since if
P(X,Y) = a0*X^2 + a1*XY + a2*Y^2
then
P(X+Y,X-Y) = (a0 + a1 + a2)*X^2 + (2*a0 - 2*a2)*XY + (a0 - a1 + a2)*Y^2
CROSSREFS
KEYWORD
easy,tabf,sign
AUTHOR
Ilia Smilga (ilia.smilga(AT)orange.fr), Feb 14 2008, Feb 20 2008
STATUS
approved