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A182436
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Triangle T(n,k), read by rows, given by (2, -1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
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0
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1, 2, 1, 2, 5, 2, 4, 8, 11, 4, 4, 20, 25, 24, 8, 8, 28, 70, 69, 52, 16, 8, 60, 126, 213, 178, 112, 32, 16, 80, 288, 460, 599, 440, 240, 64, 16, 160, 472, 1128, 1489, 1600, 1056, 512, 128, 32, 208, 976, 2152, 3914, 4457, 4120, 2480, 1088, 256
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OFFSET
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0,2
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COMMENTS
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Row sums are the powers of 3.
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LINKS
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FORMULA
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G.f.: (1+2*x-y*x)/(1-2*y*x-(2+y)*x^2).
T(n,k) = 2*T(n-1,k-1) + 2*T(n-2,k) + T(n-2,k-1), T(0,0) = T(1,1) = 1, T(1,0) = T(2,0) = T(2,2) = 2, T(2,1) = 5 and T(n,k) = 0 if k<0 or if k>n.
Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A123335(n-1), A016116(n+1), A000244(n), A057087(n), A091928(n) for x = -2, -1, 0, 1, 2, 3 respectively.
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EXAMPLE
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Triangle begins :
1
2, 1
2, 5, 2
4, 8, 11, 4
4, 20, 25, 24, 8
8, 28, 70, 69, 52, 16
8, 60, 126, 213, 178, 112, 32
16, 80, 288, 460, 599, 440, 240, 64
16, 160, 472, 1128, 1489, 1600, 1056, 512, 128
32, 208, 976, 2152, 3914, 4457, 4120, 2480, 1088, 256
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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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