login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A125950 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). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

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

Table of n, a(n) for n=0..63.

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]

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]

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 *)

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 * A323088 A052954 A123505

Adjacent sequences:  A125947 A125948 A125949 * A125951 A125952 A125953

KEYWORD

nonn,easy

AUTHOR

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

EXTENSIONS

Edited by Don Reble, Mar 09 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 5 19:02 EDT 2020. Contains 335473 sequences. (Running on oeis4.)