A125950 - OEIS

%I #30 Dec 26 2022 06:08:12

%S 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,

%T 30,35,41,49,57,67,79,93,109,129,151,178,209,246,290,340,401,471,554,

%U 652,767,902,1061,1248,1468,1727,2031,2390,2810,3306,3889,4574,5381,6329

%N 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).

%C 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.

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

%H E. Ghate and E. Hironaka, <a href="https://doi.org/10.1090/S0273-0979-01-00902-8">The Arithmetic And Geometry Of Salem Numbers</a>, Bull. Amer. Math. Soc. 38 (2001), 293-314.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SalemConstants.html">MathWorld: Salem Constants</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SubstitutionSystem.html">MathWorld: Substitution System</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,1,1,1,1,1,0,-1,-1). [From _R. J. Mathar_, Jun 30 2010]

%F 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]

%t 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 *)

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

%K nonn,easy

%O 0,11

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

%E Edited by _Don Reble_, Mar 09 2007