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Search: id:A077606
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| A077606 |
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Left differencing matrix, D, by antidiagonals. |
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+0
2
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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; listen)
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OFFSET
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1,1
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COMMENT
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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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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 (FrankTAW(AT)Netscape.net), 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: A118009 A113429 A133100 this_sequence A004601 A114915 A074711
Adjacent sequences: A077603 A077604 A077605 this_sequence 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 (ck6(AT)evansville.edu), Nov 11 2002
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