A017401 a(n) = 11n + 1.

1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 133, 144, 155, 166, 177, 188, 199, 210, 221, 232, 243, 254, 265, 276, 287, 298, 309, 320, 331, 342, 353, 364, 375, 386, 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Sequence lists all nonnegative solutions to x^k == 1 (mod 11), where k is a member of A045572. - Bruno Berselli, Jan 18 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008593, A017281, A017413.

Programs

Magma

[11*n+1: n in [0..60]]; // Vincenzo Librandi, Jul 30 2011

Mathematica

Range[1, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)

PARI

a(n)=11*n+1 \\ Charles R Greathouse IV, Jan 18 2016

Formula

G.f.: (1+10*x)/(1-x)^2.

E.g.f.: exp(x)*(1 + 11*x). - Stefano Spezia, Oct 08 2022