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A185018
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Inverse to sequence matrix for natural numbers.
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9
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1, -2, 1, 1, -2, 1, 0, 1, -2, 1, 0, 0, 1, -2, 1, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1
(list;
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OFFSET
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0,2
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COMMENTS
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Riordan array ((1-x)^2,x). Inverse matrix is Riordan array (1/(1-x)^2,x), A004736. Row sums are (1,-1,0,0,0,0,0,0,0,0,0,...). Diagonal sums are (1,-2,2,-2,2,-2,2,-2,2,-2,2,...).
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LINKS
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FORMULA
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T(n,n)=1, T(n,n-1)=-2, T(n,n-2)=1, T(n,k)=0 where k<n-2.
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EXAMPLE
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Triangle begins :
1 ;
-2, 1 ;
1, -2, 1 ;
0, 1, -2, 1 ;
0, 0, 1, -2, 1 ;
0, 0, 0, 1, -2, 1 ;
0, 0, 0, 0, 1, -2, 1 ;
0, 0, 0, 0, 0, 1, -2, 1 ;
0, 0, 0, 0, 0, 0, 1, -2, 1 ;
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MATHEMATICA
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Array[PadLeft[{1, -2, 1}, #] &, 15] (* Paolo Xausa, Jun 27 2024 *)
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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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