cp's OEIS Frontend

A210239 Triangle, read by rows, given by (2, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

%I A210239 #8 Aug 08 2015 09:27:08
%S A210239 1,2,2,2,5,3,2,9,12,5,2,13,28,25,8,2,17,52,74,50,13,2,21,84,167,177,
%T A210239 96,21,2,25,124,320,470,397,180,34,2,29,172,549,1041,1211,850,331,55,
%U A210239 2,33,228,870,2034,3042,2928,1758,600,89
%N A210239 Triangle, read by rows, given by (2, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%F A210239 G.f.: (1+x+y*x)/(1-x-y*x-y*x^2-y^2*x^2).
%F A210239 T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k-1) + T(n-2,k-2), T(0,0) = 1, T(1,0) = T(1,1) = 2 and T(n,k) = 0 if k<0 or if k>n.
%F A210239 Sum_{k, 0<=k<=n} T(n,k)*x^k = A122803(n), A000007(n), A040000(n), A026150(n+1) for x = -2, -1, 0, 1 respectively.
%F A210239 T(n,n) = Fibonacci(n+2) = A000045(n+2), T(n+1,n) = A067331(n).
%e A210239 Triangle begins :
%e A210239 1
%e A210239 2, 2
%e A210239 2, 5, 3
%e A210239 2, 9, 12, 5
%e A210239 2, 13, 28, 25, 8
%e A210239 2, 17, 52, 74, 50, 13
%e A210239 2, 21, 84, 167, 177, 96, 21
%e A210239 2, 25, 124, 320, 470, 397, 180, 34
%Y A210239 Cf. A000045, A026150, A112087 (3rd column, n>2).
%K A210239 easy,nonn,tabl
%O A210239 0,2
%A A210239 _Philippe Deléham_, Mar 19 2012