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Search: id:A144113
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| A144113 |
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Weight array W={w(i,j)} of the natural number array A038722. |
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+0
1
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| 1, 2, 1, 3, 1, 2, 4, 1, 1, 3, 5, 1, 1, 1, 4, 6, 1, 1, 1, 1, 5, 7, 1, 1, 1, 1, 1, 6, 8, 1, 1, 1, 1, 1, 1, 7, 9, 1, 1, 1, 1, 1, 1, 1, 8, 10, 1, 1, 1, 1, 1, 1, 1, 1, 9, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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In general, let w(i,j) be the weight of the unit square labeled by its
northeast vertex (i,j) and for each (m,n), define
S(m,n)=SUM{SUM{w(i,j), i=1,2,...,m, j=1,2,...,n}.
Then S(m,n) is the weight of the rectangle [0,m]x[0,n]. We call W the weight
array of S and we call S the accumulation array of W. For the case at hand, S is
the array of natural numbers having the following antidiagonals:
(1), then (3,2), then (6,5,4), then (10,9,8,7) and so on.
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FORMULA
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row 1: A000027
row n: n-1 followed by A000012, for n>1.
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EXAMPLE
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S(2,4)=1+1+2+3+2+1+1+1=14.
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CROSSREFS
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A000012, A000027, A144112.
Sequence in context: A014673 A085392 A089384 this_sequence A165416 A057059 A162306
Adjacent sequences: A144110 A144111 A144112 this_sequence A144114 A144115 A144116
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Sep 11 2008
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