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%I #34 Oct 08 2022 11:23:28
%S 1,12,23,34,45,56,67,78,89,100,111,122,133,144,155,166,177,188,199,
%T 210,221,232,243,254,265,276,287,298,309,320,331,342,353,364,375,386,
%U 397,408,419,430,441,452,463,474,485,496,507,518,529,540,551,562,573,584,595,606,617,628,639,650,661
%N a(n) = 11n + 1.
%C Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=11, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=2, a(n-1)=-charpoly(A,x^(n-1)). - _Milan Janjic_, Feb 21 2010
%C Sequence lists all nonnegative solutions to x^k == 1 (mod 11), where k is a member of A045572. - _Bruno Berselli_, Jan 18 2016
%H Vincenzo Librandi, <a href="/A017401/b017401.txt">Table of n, a(n) for n = 0..5000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F G.f.: (1+10*x)/(1-x)^2.
%F E.g.f.: exp(x)*(1 + 11*x). - _Stefano Spezia_, Oct 08 2022
%t Range[1, 1000, 11] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)
%o (Magma) [11*n+1: n in [0..60]]; // _Vincenzo Librandi_, Jul 30 2011
%o (PARI) a(n)=11*n+1 \\ _Charles R Greathouse IV_, Jan 18 2016
%Y Cf. A008593, A017281, A017413.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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