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Search: id:A087465
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| A087465 |
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Rank array R of 3/2 read by antidiagonals; this array is the dispersion of the complement of the sequence given by r(n)=r(n-1)+1+[3n/2] for n>=1, with r(0)=1; that is, A077043(n+1). |
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+0
5
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| 1, 2, 3, 4, 5, 7, 6, 8, 10, 12, 9, 11, 14, 16, 19, 13, 15, 18, 21, 24, 27, 17, 20, 23, 26, 30, 33, 37, 22, 25, 29, 32, 36, 40, 44, 48, 28, 31, 35, 39, 43, 47, 52, 56, 61, 34, 38, 42, 46, 51, 55, 60, 65, 70, 75, 41, 45, 50, 54, 59, 64, 69, 74, 80, 85, 91, 49, 53, 58, 63, 68, 73
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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The sequence is a permutation of the natural numbers, and the array is a transposable dispersion.
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LINKS
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Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7, 2004.
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FORMULA
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R(i, j)=R(i, 0)+R(0, j)+ij-1, i>=0, j>=0.
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EXAMPLE
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Northwest corner of R:
1 2 4 6 9
3 5 8 11 15
7 10 14 18 23
12 16 21 26 32
19 24 30 36 43
Let t=3/2; then R(i,j)=rank of (j,i) when all (a,b) are ranked by the relation << defined as follows:
(a,b)<<(c,d) if a+bt<c+dt, and (a,b)<<(c,d) if a+bt=c+dt and b<d.
Thus R(2,1)=10 is the rank of (1,2) in the list
(0,0)<<(1,0)<<(0,1)<<(2,0)<<(1,1)<<(3,0)<<(0,2)<<(2,1)<<(4,0)<<(1,2).
In general R(i,j) is the last position occupied by j+it when all a+bj are ranked under ordinary <=.
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CROSSREFS
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Cf. A087466, A087468, A087483, A087484, A087489.
Sequence in context: A095903 A088750 A056018 this_sequence A056017 A091995 A066937
Adjacent sequences: A087462 A087463 A087464 this_sequence A087466 A087467 A087468
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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 09 2003
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