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Search: id:A004736
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| A004736 |
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Triangle T(n,k) = n-k, n >= 1, 0<=k<n. Fractal sequence formed by repeatedly appending strings m m-1 . . . 2 1. |
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+0
48
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| 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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"Smarandache Decrescendo Subsequences".
The PARI functions t1, t2 can be used to read a square array T(n,k) (n >= 1, k >= 1) by antidiagonals upwards: n -> T(t1(n), t2(n)). - Michael Somos, Aug 23, 2002
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REFERENCES
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C. Kimberling, "Numeration systems and fractal sequences," Acta Arithmetica 73 (1995) 103-117.
F. Smarandache, "Collected Papers", Vol. II, Tempus Publ. Hse., Bucharest, 1996; F. Smarandache, "Numerical Sequences", University of Craiova, 1975; [ See Arizona State University, Special Collection, Tempe, AZ, USA ].
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, Phoenix, 2006.
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LINKS
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C. Kimberling, Fractal sequences
M. L. Perez et al., eds., Smarandache Notions Journal
F. Smarandache, Collected Papers, Vol. II
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
M. Somos, Sequences used for indexing triangular or square arrays
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) = (2 - 2 n + round(SQRT(2 n)) + round(SQRT(2 n))^2)/2. E.g. a(47) = 9. - Brian Tenneson (phoenix(AT)alephnulldimension.net), Oct 11 2003
G.f.: 1 / [(1-x)^2 * (1-xy) ]. - R. Stephan, Jan 23 2005
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EXAMPLE
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1; 2,1; 3,2,1; 4,3,2,1; 5,4,3,2,1; ...
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MATHEMATICA
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Flatten[ Table[ Reverse[ Range[n]], {n, 12}]] (from Robert G. Wilson v Apr 27 2004)
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PROGRAM
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(PARI) a(n)=1+binomial(1+floor(1/2+sqrt(2*n)), 2)-n
(PARI) t1(n)=binomial(floor(3/2+sqrt(2*n)), 2)-n+1 /* A004736 */
(PARI) t2(n)=n-binomial(floor(1/2+sqrt(2*n)), 2) /* A002260 */
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CROSSREFS
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a(n+1)=1+A025581(n). Cf. A002262, A025581, A003056.
Ordinal transform of A002260.
Adjacent sequences: A004733 A004734 A004735 this_sequence A004737 A004738 A004739
Sequence in context: A057058 A088643 A102482 this_sequence A023122 A052310 A052313
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KEYWORD
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nonn,easy,tabl,nice
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AUTHOR
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R. Muller
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