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A208324
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Triangle T(n,k), read by rows, given by (2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (4, -2, 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, 4, 3, 10, 8, 4, 18, 28, 16, 5, 28, 64, 72, 32, 6, 40, 120, 200, 176, 64, 7, 54, 200, 440, 576, 416, 128, 8, 70, 308, 840, 1456, 1568, 960, 256, 9, 88, 448, 1456, 3136, 4480, 4096, 2176, 512, 10, 108, 624, 2352, 6048, 10752, 13056, 10368, 4864
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OFFSET
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0,2
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COMMENTS
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Compare this sequence with A207627.
Column k is divisible by 2^k.
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LINKS
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FORMULA
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T(n,0) = n+1.
T(n,1) = 2*T(n,0) + T(n-1,1).
T(n,k) = 2*T(n-1,k-1) + T(n-1,k) for k>1.
T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-2,k-1) with T(0,0) = 1, T(1,0) = 2, T(1,1) = 4.
G.f.: (1+2*y*x)/(1-2*(1+y)*x+(1+2*y)*x^2).
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EXAMPLE
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Triangle begins :
1
2, 4
3, 10, 8
4, 18, 28, 16
5, 28, 64, 72, 32
6, 40, 120, 200, 176, 64
7, 54, 200, 440, 576, 416, 128
8, 70, 308, 840, 1456, 1568, 960, 256
9, 88, 448, 1456, 3136, 4480, 4096, 2176, 512
10, 108, 624, 2352, 6048, 10752, 13056, 10368, 4864, 1024
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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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