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A035486
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Kimberling's expulsion array read by antidiagonals.
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7
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1, 2, 2, 3, 3, 4, 4, 4, 2, 6, 5, 5, 5, 2, 8, 6, 6, 6, 7, 7, 6, 7, 7, 7, 4, 9, 2, 13, 8, 8, 8, 8, 2, 11, 12, 2, 9, 9, 9, 9, 10, 9, 8, 11, 18, 10, 10, 10, 10, 6, 12, 9, 16, 17, 16, 11, 11, 11, 11, 11, 7, 14, 14, 12, 14, 23, 12, 12, 12, 12, 12, 13, 11, 6, 9, 21, 2, 13, 13, 13, 13, 13, 13, 8, 15
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| To get next row, start with element to right of diagonal term, then take number to left of diagonal, then back to 2nd number to right, etc.
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REFERENCES
| R. K. Guy, Unsolved Problems Number Theory, Sect E35.
C. Kimberling, Problem 1615, Crux Mathematicorum, Vol. 17 (2) 44 1991 and Vol. 18, March 1992, p. 82-83.
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LINKS
| E. Perez Herrero, Table of n, a(n) for n=1..10000
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EXAMPLE
| 1 2 3 4 5 6 7 8 9 10...
2 3 4 5 6 7 8 9 10 11...
4 2 5 6 7 8 9 10 11 12...
6 2 7 4 8 9 10 11 12 13...
8 7 9 2 10 6 11 12 13 14...
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MATHEMATICA
| Contribution from Enrique Perez Herrero (psychgeometry(AT)gmail.com), Mar 30 2010: (Start)
K[i_, j_] := i + j - 1 /; (j >= 2 i - 3);
K[i_, j_] := K[i - 1, i - (j + 2)/2] /; (EvenQ[j] && (j < 2 i - 3));
K[i_, j_] := K[i - 1, i + (j - 1)/2] /; (OddQ[j] && (j < 2 i - 3));
K[i_] := K[i] = K[i, i]; SetAttributes[K, Listable];
T[n_] := n*(n + 1)/2;
S[n_] := Floor[1/2 (1 + Sqrt[1 + 8 (n - 1)])];
AJ[n_] := 1 + T[S[n]] - n;
AI[n_] := 1 + S[n] - AJ[n];
A035486[n_] := K[AI[n], AJ[n]]; (End)
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CROSSREFS
| Cf. A006852, A007063, A038807.
A175312 [From Enrique Perez Herrero (psychgeometry(AT)gmail.com), Mar 30 2010]
Sequence in context: A085654 A074719 A079730 * A172397 A143489 A130249
Adjacent sequences: A035483 A035484 A035485 * A035487 A035488 A035489
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KEYWORD
| nonn,tabl,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999
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