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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.

%I A202396 #10 Sep 08 2013 19:59:29
%S A202396 1,2,2,5,8,3,13,27,19,5,34,86,86,42,8,89,265,338,234,85,13,233,798,
%T A202396 1227,1084,567,166,21,610,2362,4230,4510,3038,1286,314,34,1597,6898,
%U A202396 14058,17474,14284,7814,2774,582,55
%N 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.
%C A202396 T(n,n) = Fibonacci(n+2) = A000045(n+2).
%F A202396 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<k.
%F A202396 G.f.: (1+(y-1)*x)/(1-(3+y)*x+(1-y^2)*x^2).
%F A202396 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.
%F A202396 Sum_{k, 0<=k<=n} T(n,k)*3^k = 2^n * A055099(n). - _Philippe Deléham_, Feb 05 2012
%e A202396 Triangle begins :
%e A202396 1
%e A202396 2, 2
%e A202396 5, 8, 3
%e A202396 13, 27, 19, 5
%e A202396 34, 86, 86, 42, 8
%e A202396 89, 265, 338, 234, 85, 13
%Y A202396 Cf. A000045, A001519, A122367, A000302 (row sums), A202395
%K A202396 nonn,tabl
%O A202396 0,2
%A A202396 _Philippe Deléham_, Dec 18 2011