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A208532 Mirror image of triangle in A125185; unsigned version of A120058.

%I A208532 #7 Feb 22 2013 14:40:30
%S A208532 1,2,1,3,4,2,4,9,10,4,5,16,28,24,8,6,25,60,80,56,16,7,36,110,200,216,
%T A208532 128,32,8,49,182,420,616,560,288,64,9,64,280,784,1456,1792,1408,640,
%U A208532 128,10,81,408,1344,3024,4704,4992,3456,1408,256
%N A208532 Mirror image of triangle in A125185; unsigned version of A120058.
%C A208532 Subtriangle of the triangle given by (1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C A208532 Equals A007318*A134309*A097806 as infinite lower triangular matrix.
%C A208532 Row sums are powers of 3 (A000244).
%C A208532 Diagonal sums are powers of 2 (A000079).
%F A208532 T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-1,k-1), T(0,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.
%F A208532 G.f.: (1-y*x)/((1-x)*(1-(1+2*y)*x)).
%F A208532 Sum_{k, 0<=k<=n} T(n,k)*x^k = A083085(n), A084567(n), A000012(n), A000027(n+1), A000244(n), A083065(n), A083076(n) for x = -3, -2, -1, 0, 1, 2, 3 respectively.
%e A208532 Triangle begins :
%e A208532 1
%e A208532 2, 1
%e A208532 3, 4, 2
%e A208532 4, 9, 10, 4
%e A208532 5, 16, 28, 24, 8
%e A208532 6, 25, 60, 80, 56, 16
%e A208532 7, 36, 110, 200, 216, 128, 32
%e A208532 8, 49, 182, 420, 616, 560, 288, 64
%e A208532 9, 64, 280, 784, 1456, 1792, 1408, 640, 128
%e A208532 10, 81, 408, 1344, 3024, 4704, 4992, 3456, 1408, 256
%e A208532 Triangle (1, 1, -1, 1, 0, 0, 0, ...) DELTA (0, 1, 1, 0, 0, 0, ...) begins :
%e A208532 1
%e A208532 1, 0
%e A208532 2, 1, 0
%e A208532 3, 4, 2, 0
%e A208532 4, 9, 10, 4, 0
%e A208532 5, 16, 28, 24, 8, 0
%e A208532 6, 25, 60, 80, 56, 16, 0
%Y A208532 Cf. Columns: A000027, A000290, A006331, A112742.
%Y A208532 Cf. Diagonals: A011782, 2*A045623,
%K A208532 easy,nonn,tabl
%O A208532 0,2
%A A208532 _Philippe Deléham_, Feb 27 2012