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A125950
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a(0) to a(9) = 1; a(n+10) = -a(n+9) + a(n+7) + a(n+6) + a(n+5) + a(n+4) + a(n+3) - a(n+1) - a(n).
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2
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 7, 8, 10, 11, 13, 16, 18, 22, 25, 30, 35, 41, 49, 57, 67, 79, 93, 109, 129, 151, 178, 209, 246, 290, 340, 401, 471, 554, 652, 767, 902, 1061, 1248, 1468, 1727, 2031, 2390, 2810, 3306, 3889, 4574, 5381, 6329
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,11
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COMMENTS
| a(n) = O(n^c), where c is the larger real root of x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1, 1.176280818..., the smallest known Salem constant.
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REFERENCES
| Wolfram, S., A New Kind of Science. Champaign, IL: Wolfram Media, pp. 82-92, 2002.
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LINKS
| Eric Weisstein's World of Mathematics, MathWorld: Salem Constants
Eric Weisstein's World of Mathematics, MathWorld: Substitution System
Author?, Bulletin (New Series) AMS, The Arithmetic And Geometry Of Salem Numbers
Index to sequences with linear recurrences with constant coefficients, signature (-1,0,1,1,1,1,1,0,-1,-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 30 2010]
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FORMULA
| G.f.: ( 1+2*x+2*x^2+x^3-x^5-2*x^6-3*x^7-3*x^8-2*x^9 ) / ( 1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10 ). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 30 2010]
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CROSSREFS
| Cf. Coefficients of Lehmer's polynomial A070178, Inverse of Salem polynomial A029826, Heptic Salem vector Markov sequence A107480, 9th order Fibonacci sequence A127193, 10th order Fibonacci sequence A127194, 11th order Fibonacci sequence A127624.
Sequence in context: A117875 A084840 A029278 * A052954 A123505 A114920
Adjacent sequences: A125947 A125948 A125949 * A125951 A125952 A125953
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KEYWORD
| nonn
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AUTHOR
| Luis A Restrepo (luisiii(AT)mac.com), Feb 04 2007
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EXTENSIONS
| Edited by Don Reble (djr(AT)nk.ca), Mar 09 2007
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