A125950 a(0)=a(1)=...=a(9)=1; a(n) = - a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7) - a(n-9) - a(n-10).

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

Offset: 0

Author

Luis A Restrepo (luisiii(AT)mac.com), Feb 04 2007

Keywords

• nonn
• easy

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.

References

• Wolfram, S., A New Kind of Science. Champaign, IL: Wolfram Media, pp. 82-92, 2002.

Links

• E. Ghate and E. Hironaka, The Arithmetic And Geometry Of Salem Numbers, Bull. Amer. Math. Soc. 38 (2001), 293-314.
• Eric Weisstein's World of Mathematics, MathWorld: Salem Constants
• Eric Weisstein's World of Mathematics, MathWorld: Substitution System
• Index entries for linear recurrences with constant coefficients, signature (-1,0,1,1,1,1,1,0,-1,-1). [From _R. J. Mathar_, Jun 30 2010]

Crossrefs

Cf. A070178, A029826, A107480, A127193, A127194, A127624.

Programs

Mathematica

LinearRecurrence[{-1,0,1,1,1,1,1,0,-1,-1},{1,1,1,1,1,1,1,1,1,1},70] (* Harvey P. Dale, May 31 2013 *)

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 ). [R. J. Mathar, Jun 30 2010]

Extensions

Edited by Don Reble, Mar 09 2007