A017509 a(n) = 11*n + 10.

10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 120, 131, 142, 153, 164, 175, 186, 197, 208, 219, 230, 241, 252, 263, 274, 285, 296, 307, 318, 329, 340, 351, 362, 373, 384, 395, 406, 417, 428, 439, 450, 461, 472, 483, 494, 505, 516, 527, 538, 549, 560, 571, 582

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

If k is any member of A045572, the sequence lists the numbers n such that (n^k+1)/11 is a nonnegative integer. See also A267541. - Bruno Berselli, Jan 16 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Tanya Khovanova, Recursive Sequences
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 989
• Leo Tavares, Illustration: Triangular Lines
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008593, A017401, A017413, A045572, A267541.

Cf. A211013 (partial sums), A254322 (partial products).

Powers of the form (11*n+10)^m: this sequence (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

Cf. A008591, A005408.

Programs

GAP

List([0..60], n-> (11*n+10)); # G. C. Greubel, Oct 29 2019

Magma

[11*n+10: n in [0..60]]; // Vincenzo Librandi, Sep 18 2011

Maple

seq((11*n+10), n=0..60); # G. C. Greubel, Oct 29 2019

Mathematica

Range[10, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 29 2011 *)
(11*Range[60] -1) (* G. C. Greubel, Oct 29 2019 *)

PARI

a(n)=11*n+10 \\ Charles R Greathouse IV, Jul 10 2016

Python

def a(n): return 11*n + 10
print([a(n) for n in range(53)]) # Michael S. Branicky, Oct 21 2021

Sage

[(11*n+10) for n in (0..60)] # G. C. Greubel, Oct 29 2019

Formula

From G. C. Greubel, Oct 29 2019: (Start)

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

E.g.f.: (10 + 11*x)*exp(x).

a(n) = 2*a(n-1) - a(n-2). (End)

a(n) = A008591(n+1) + A005408(n). - Leo Tavares, Oct 25 2022