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A181974 Triangle T(n,k), read by rows, given by (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -3, 2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 0

%I

%S 1,1,1,2,3,1,3,4,2,1,5,7,5,4,1,8,11,10,9,3,1,13,18,20,20,9,5,1,21,29,

%T 38,40,22,15,4,1,34,47,71,78,51,40,14,6,1,55,76,130,147,111,95,40,22,

%U 5,1,89,123,235,272,233,213,105,68,20,7,1

%N Triangle T(n,k), read by rows, given by (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -3, 2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

%F G.f.: (1+y*x+2*y*x^2)/(1-x-x^2-y^2*x^2).

%F T(n,k) = T(n-1,k) + T(n-2,k) + T(n-2,k-2), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 2, T(2,1) = 3 and T(n,k) = 0 if k<0 or if k>n.

%F T(n + 2k, 2k) = A037027(n + k, k).

%F T(n + 2k +1, 2k + 1) = A182001(n + k, k).

%F T(n,0) = Fibonacci(n+1).

%e Triangle begins :

%e 1

%e 1, 1

%e 2, 3, 1

%e 3, 4, 2, 1

%e 5, 7, 5, 4, 1

%e 8, 11, 10, 9, 3, 1

%e 13, 18, 20, 20, 9, 5, 1

%e 21, 29, 38, 40, 22, 15, 4, 1

%e 34, 47, 71, 78, 51, 40, 14, 6, 1

%e 55, 76, 130, 147, 111, 95, 40, 22, 5, 1

%e 89, 123, 235, 272, 233, 213, 105, 68, 20, 7, 1

%e 144, 199, 420, 495, 474, 455, 256, 185, 65, 30, 6, 1

%Y Cf. Columns : A000045, A000032, A001629, A023607, A001628, A152881, A001872, A001873

%K easy,nonn,tabl

%O 0,4

%A _Philippe Deléham_, Apr 06 2012

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Last modified April 11 10:11 EDT 2021. Contains 342886 sequences. (Running on oeis4.)