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A079500
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Number of compositions of the integer n in which the first part is >= the other parts.
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16
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1, 1, 2, 3, 5, 8, 14, 24, 43, 77, 140, 256, 472, 874, 1628, 3045, 5719, 10780, 20388, 38674, 73562, 140268, 268066, 513350, 984911, 1892875, 3643570, 7023562, 13557020, 26200182, 50691978, 98182666, 190353370, 369393466, 717457656, 1394632365, 2713061899
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| In dismal arithmetic in base 2, this is the number of dismal divisors of the number 111...1 (with n 1's). E.g. 1111 has a(4) = 5 divisors (see A048888). - N. J. A. Sloane, Feb 23 2011.
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REFERENCES
| A. Frosini and S. Rinaldi, On the Sequence A079500 and Its Combinatorial Interpretations, Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.1.
R. Kemp, Balanced ordered trees, Random Structures and Alg., 5 (1994), pp. 99-121.
Arnold Knopfmacher and Neville Robbins, Compositions with parts constrained by the leading summand, Ars Combin. 76 (2005), 287-295.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..399
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic
A. Frosini and S. Rinaldi, On the Sequence A079500 and Its Combinatorial Interpretations, Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.1.
Index entries for sequences related to dismal arithmetic
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FORMULA
| G.f.: (1-z) * Sum_{k=1..oo}z^k/(1-2z+z^k).
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EXAMPLE
| a(4)=3 because we have 4;3+1;2+2,2+1+1;1+1+1+1
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MAPLE
| M:=101:
t1:=add( (1-x)*x^k/(1-2*x+x^k), k=1..M):
series(t1, x, M-1);
seriestolist(%);
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CROSSREFS
| Essentially the same as A007059.
This is a subsequence of A067399: A067399(2^k-1).
First differences of A186537. - N. J. A. Sloane, Feb 23 2011
Cf. A188541. Equals A048888(n)-1.
Sequence in context: A108351 A038495 A007059 * A108296 A072100 A104882
Adjacent sequences: A079497 A079498 A079499 * A079501 A079502 A079503
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KEYWORD
| nonn
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AUTHOR
| Arnold Knopfmacher (arnoldk(AT)cam.wits.ac.za), Jan 21 2003
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EXTENSIONS
| Offset corrected by N. J. A. Sloane, Feb 23 2011
More terms from N. J. A. Sloane, Feb 24 2011
Further edits (required in order to clarify the definition - is the first part >= the rest. or only > the rest? Answer: the former; for the latter, see A007059) by N. J. A. Sloane, May 08 2011
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