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A018902
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a(n+2) = 5a(n+1) - 3a(n).
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3
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1, 4, 17, 73, 314, 1351, 5813, 25012, 107621, 463069, 1992482, 8573203, 36888569, 158723236, 682950473, 2938582657, 12644061866, 54404561359, 234090621197, 1007239421908, 4333925245949, 18647907964021
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Define the sequence S(a_0,a_1) by a_{n+2} is the least integer such that a_{n+2}/a_{n+1}>a_{n+1}/a_n for n >= 0. This is S(1,4).
a(n) is the number of compositions of n when there are 4 types of ones. [From Milan R. Janjic (agnus(AT)blic.net), Aug 13 2010]
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REFERENCES
| D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993;.
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 474
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FORMULA
| A member of the family of sequences defined by a(n) = (a_1+1)a(n-1) - (a_1-1)a(n-2). Alternatively, invert A007052 (invert: define b by 1+Sum a(n)x^n = 1/(1 - Sum b(n)x^n)).
a(n+1)a(n+1) - a(n+2)a(n) = -3^n, n > 0. - Douglas Rogers, Jul 11 2004.
O.g.f.: (1-x)/(1-5*x+3*x^2) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
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MATHEMATICA
| LinearRecurrence[{5, -3}, {1, 4}, 40] (* From Harvey P. Dale, Jan 14 2012 *)
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CROSSREFS
| Equals (1/3) A081704(n+1).
Sequence in context: A113442 A085732 A083330 * A095940 A184700 A125586
Adjacent sequences: A018899 A018900 A018901 * A018903 A018904 A018905
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KEYWORD
| nonn
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AUTHOR
| R. K. Guy (rkg(AT)cpsc.ucalgary.ca), N. J. A. Sloane (njas(AT)research.att.com).
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