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A077606
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Left differencing matrix, D, by antidiagonals.
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1
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1, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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If v is a sequence written as a column vector, then Dv is the sequence of first differences of v. The inverse of D is the left summing matrix; the transpose of D is the right differencing matrix.
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LINKS
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Table of n, a(n) for n=1..108.
C. Kimberling, Matrix Transformations of Integer Sequences, J. Integer Seqs., Vol. 6, 2003.
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FORMULA
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D(n, n-1)=-1, D(n, n)=1, else D(n, k)=0.
As a sequence, a(2k^2-2k+1) = 1, a(2k^2) = -1, otherwise a(n) = 0. - Franklin T. Adams-Watters, Jan 12 2007
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EXAMPLE
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Northwest corner:
1 0 0 0 0
-1 1 0 0 0
0 -1 1 0 0
0 0 -1 1 0
0 0 0 -1 1
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CROSSREFS
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Cf. A077605.
Cf. A001844, A001105.
Sequence in context: A113429 A133100 A216230 * A004601 A114915 A074711
Adjacent sequences: A077603 A077604 A077605 * A077607 A077608 A077609
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Clark Kimberling, Nov 11 2002
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STATUS
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approved
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