A161705 a(n) = 18*n + 1.

1, 19, 37, 55, 73, 91, 109, 127, 145, 163, 181, 199, 217, 235, 253, 271, 289, 307, 325, 343, 361, 379, 397, 415, 433, 451, 469, 487, 505, 523, 541, 559, 577, 595, 613, 631, 649, 667, 685, 703, 721, 739, 757, 775, 793, 811, 829, 847, 865, 883, 901, 919, 937, 955

Offset: 0

Author

Reinhard Zumkeller, Jun 17 2009

Keywords

• nonn
• easy

Comments

Digital root of a(n) is 1. - Alexander R. Povolotsky, Jun 13 2012

These numbers can be written as the sum of four integer cubes as a(n) = (2*n + 14)^3 + (3*n + 30)^3 + (- 2*n - 23)^3 + (- 3*n - 26)^3. - Arkadiusz Wesolowski, Aug 15 2013

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A005408, A016813, A016921, A017281, A017533, A128470, A158057, A161700, A161709, A161714, A287326 (fourth column).

Cf. A016777, A017173.

Programs

GAP

List([0..60], n-> 18*n+1); # G. C. Greubel, Sep 18 2019

Magma

[18*n +1: n in [0..60]]; // G. C. Greubel, Sep 18 2019

Maple

seq(18*n+1, n=0..60); # G. C. Greubel, Sep 18 2019

Mathematica

Range[1, 1000, 18] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)
LinearRecurrence[{2,-1},{1,19}, 60] (* G. C. Greubel, Feb 17 2017 *)

PARI

vector(60, n, 18*n-17) \\ G. C. Greubel, Feb 17 2017

Sage

[18*n+1 for n in (0..60)] # G. C. Greubel, Sep 18 2019

Formula

a(n) = 18*n + 1, n >= 0.

a(n) = a(n-1) + 18 (with a(0)=1). - Vincenzo Librandi, Dec 27 2010

From G. C. Greubel, Feb 17 2017: (Start)

G.f.: (1 + 17*x)/(1-x)^2.

E.g.f.: (1 + 18*x)*exp(x).

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

a(n) = A017173(2*n) = A016777(6*n). - Elmo R. Oliveira, Apr 12 2025