login
Inverse of number triangle A070909.
2

%I #16 Aug 26 2021 21:28:10

%S 1,-1,1,-1,0,1,0,0,-1,1,0,0,-1,0,1,0,0,0,0,-1,1,0,0,0,0,-1,0,1,0,0,0,

%T 0,0,0,-1,1,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,

%U -1,0,1

%N Inverse of number triangle A070909.

%C Generalized (conditional) Riordan array with k-th column generated by x^k*(1-x-x^2) if k is even, x^k otherwise.

%C Triangle T(n,k), read by rows, given by (-1,2,-1/2,-1/2,0,0,0,0,0,0,0,...) DELTA (1,0,-1,0,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Nov 19 2011

%C Double Riordan array (1 - x - x^2; x/(1 - x - x^2), x*(1 - x - x^2)) as defined in Davenport et al. - _Peter Bala_, Aug 15 2021

%H D. E. Davenport, L. W. Shapiro and L. C. Woodson, <a href="https://doi.org/10.37236/2034">The Double Riordan Group</a>, The Electronic Journal of Combinatorics, 18(2) (2012).

%F G.f.: (1+(y-1)*x-x^2)/((1-y*x)*(1+y*x)). - _Philippe Deléham_, Nov 19 2011

%e Triangle begins

%e 1,

%e -1, 1,

%e -1, 0, 1,

%e 0, 0, -1, 1,

%e 0, 0, -1, 0, 1,

%e 0, 0, 0, 0, -1, 1,

%e 0, 0, 0, 0, -1, 0, 1,

%e 0, 0, 0, 0, 0, 0, -1, 1,

%e 0, 0, 0, 0, 0, 0, -1, 0, 1,

%e 0, 0, 0, 0, 0, 0, 0, 0, -1, 1,

%e 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1

%e Production matrix begins

%e -1, 1,

%e -2, 1, 1,

%e -1, 1, -1, 1,

%e -1, 1, -2, 1, 1,

%e -1, 1, -1, 1, -1, 1,

%e -1, 1, -1, 1, -2, 1, 1,

%e -1, 1, -1, 1, -1, 1, -1, 1,

%e -1, 1, -1, 1, -1, 1, -2, 1, 1,

%e -1, 1, -1, 1, -1, 1, -1, 1, -1, 1

%Y Cf. A084221, A084938.

%K easy,sign,tabl

%O 0,1

%A _Paul Barry_, Nov 03 2010