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A216344
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Triangle T(n,k), read by rows, given by (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, -1, 1, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938 .
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0
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1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 4, 4, 3, 1, 0, 8, 8, 7, 4, 1, 0, 16, 16, 16, 11, 5, 1, 0, 32, 32, 36, 28, 16, 6, 1, 0, 64, 64, 80, 68, 45, 22, 7, 1, 0, 128, 128, 176, 160, 118, 68, 29, 8, 1, 0, 256, 256, 384
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OFFSET
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0,8
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LINKS
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FORMULA
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G.f.: (1-2*x+y*x^2)/(1-2*x-y*x+2*y*x^2-y^2*x^3)
T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k-1) + T(n-3,k-2), T(0,0) = T(1,1) = T(2,1) = T(2,2) = 1, T(1,0) = T(2,0) = 0 and T(n,k) = 0 if k<0 or if k>n .
Sum_{k, 0<=k<=n} T(n,k) = A034943(n+1) .
Sum_{k, 0<=k<=n} T(n,k)*2^k*(-1/2)^(n-k) = A052955(n) .
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EXAMPLE
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Triangle begins :
1
0, 1
0, 1, 1
0, 2, 2, 1
0, 4, 4, 3, 1
0, 8, 8, 7, 4, 1
0, 16, 16, 16, 11, 5, 1
0, 32, 32, 36, 28, 16, 6, 1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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