A202396 Triangle T(n,k), read by rows, given by (2, 1/2, 1/2, 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.
1, 2, 2, 5, 8, 3, 13, 27, 19, 5, 34, 86, 86, 42, 8, 89, 265, 338, 234, 85, 13, 233, 798, 1227, 1084, 567, 166, 21, 610, 2362, 4230, 4510, 3038, 1286, 314, 34, 1597, 6898, 14058, 17474, 14284, 7814, 2774, 582, 55
Offset: 0
Examples
Triangle begins : 1 2, 2 5, 8, 3 13, 27, 19, 5 34, 86, 86, 42, 8 89, 265, 338, 234, 85, 13
Formula
T(n,k) = 3*T(n-1,k) + T(n-1,k-1) + T(n-2,k-2) - T(n-2,k) with T(0,0) = 1, T(1,0) = T(1,1) = 2 and T(n,k) = 0 if k<0 or if n
G.f.: (1+(y-1)*x)/(1-(3+y)*x+(1-y^2)*x^2).
Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A122367(n), A000302(n), A180035(n) for x = -1, 0, 1, 2 respectively.
Sum_{k, 0<=k<=n} T(n,k)*3^k = 2^n * A055099(n). - Philippe Deléham, Feb 05 2012
Comments