A017461 a(n) = 11*n + 6.

6, 17, 28, 39, 50, 61, 72, 83, 94, 105, 116, 127, 138, 149, 160, 171, 182, 193, 204, 215, 226, 237, 248, 259, 270, 281, 292, 303, 314, 325, 336, 347, 358, 369, 380, 391, 402, 413, 424, 435, 446, 457, 468, 479, 490, 501, 512, 523, 534, 545, 556, 567, 578, 589

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008593, A017401, A017449, A141694.

Cf. similar sequences with closed form (2*k-1)*n+k listed in A269044.

Powers of the form (11*n+6)^m: this sequence (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

Programs

GAP

List([0..60], n-> 11*n+6); # G. C. Greubel, Sep 19 2019

Magma

[11*n+6: n in [0..60]]; // Vincenzo Librandi, Sep 03 2011

Maple

seq(11*n+6, n=0..60); # G. C. Greubel, Sep 19 2019

Mathematica

Range[6, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
LinearRecurrence[{2,-1},{6,17},60] (* or *) NestList[11 + #&, 6, 60] (* Harvey P. Dale, Apr 14 2015 *)

PARI

a(n)=11*n+6 \\ Charles R Greathouse IV, Oct 07 2015

Sage

[11*n+6 for n in (0..60)] # G. C. Greubel, Sep 19 2019

Formula

a(0)=6, a(1)=17; for n>1, a(n) = 2*a(n-1) - a(n-2). - Harvey P. Dale, Apr 14 2015

From G. C. Greubel, Sep 19 2019: (Start)

G.f.: (6 + 5*x)/(1-x)^2.

E.g.f.: (6 + 11*x)*exp(x). (End)

a(n) = A141694(n)/2. - Elmo R. Oliveira, Apr 11 2025