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A103452
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Inverse of number triangle A103451.
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7
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1, -1, 1, -1, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1
(list;
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Row sums are 0^n. Diagonal sums are 0^n - (1-(-1)^n)/2.
Triangle T(n,k), 0 <= k <= n, read by rows given by [ -1, 2, 0, 0, 0, 0, 0, ...] DELTA [1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, May 01 2007
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 0..10010 (Rows 0 <= n <= 140)
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FORMULA
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Number triangle T(n,k) = if(n=k, 1, if(n>0 and k=0, -1, 0)).
G.f.: (1 - 2*x + y*x^2)/((1-x)*(1-y*x)). - Philippe Deléham, Feb 11 2012
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EXAMPLE
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Rows start {1}, {-1,1}, {-1,0,1}, {-1,0,0,1}, {-1,0,0,0,1}, ....
Triangle begins
1,
-1, 1,
-1, 0, 1,
-1, 0, 0, 1,
-1, 0, 0, 0, 1,
-1, 0, 0, 0, 0, 1,
-1, 0, 0, 0, 0, 0, 1,
-1, 0, 0, 0, 0, 0, 0, 1,
-1, 0, 0, 0, 0, 0, 0, 0, 1,
-1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
Production matrix begins
-1, 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
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MATHEMATICA
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Table[Range[n] /. {k_ /; k == 1 && n != 1 -> -1, k_ /; k == n -> 1, _Integer -> 0}, {n, 15}] // Flatten (* Michael De Vlieger, Jul 21 2016 *)
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CROSSREFS
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Cf. A103453, A103454, A103455.
Sequence in context: A270885 A127972 A103451 * A131219 A127970 A158856
Adjacent sequences: A103449 A103450 A103451 * A103453 A103454 A103455
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry, Feb 06 2005
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STATUS
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approved
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