cp's OEIS Frontend

A167666 Triangle read by rows given by [1,1,-4,2,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

%I A167666 #8 Sep 08 2013 19:59:25
%S A167666 1,1,1,2,3,1,0,4,5,1,0,0,6,7,1,0,0,0,8,9,1,0,0,0,0,10,11,1,0,0,0,0,0,
%T A167666 12,13,1,0,0,0,0,0,0,14,15,1,0,0,0,0,0,0,0,16,17,1,0,0,0,0,0,0,0,0,18,
%U A167666 19,1,0,0,0,0,0,0,0,0,0,20,21,1,0,0,0,0,0,0,0,0,0,0,22,23,1,0,0,0,0,0,0,0,0
%N A167666 Triangle read by rows given by [1,1,-4,2,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
%C A167666 Row sums = A111284(n+1), Diagonal sums = A109613(n).
%F A167666 T(n,k) = 2*T(n-1,k-1) - T(n-2,k-2), T(0,0) = T(1,0) = T(1,1) = 1, T(2,0) = 2, T(2,1) = 3, T(3,0) = 0, T(3,1) = 4. - _Philippe Deléham_, Feb 18 2012
%F A167666 G.f.: (1+(1-y)*x+(2+y)*x^2)/(1-y*x)^2. - _Philippe Deléham_, Feb 18 2012
%F A167666 Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A130779(n), A111284(n+1), A167667(n), A167682(n) for x = -1, 0, 1, 2, 3 respectively. - _Philippe Deléham_, Feb 18 2012
%e A167666 Triangle begins :
%e A167666 1 ;
%e A167666 1, 1 ;
%e A167666 2, 3, 1 ;
%e A167666 0, 4, 5, 1 ;
%e A167666 0, 0, 6, 7, 1 ;
%e A167666 0, 0, 0, 8, 9, 1 ;
%e A167666 0, 0, 0, 0, 10, 11, 1 ; ...
%Y A167666 Cf. A000012, A005408, A005843
%K A167666 nonn,tabl
%O A167666 0,4
%A A167666 _Philippe Deléham_, Nov 08 2009