A190991 a(n) = 13*n + 1.

1, 14, 27, 40, 53, 66, 79, 92, 105, 118, 131, 144, 157, 170, 183, 196, 209, 222, 235, 248, 261, 274, 287, 300, 313, 326, 339, 352, 365, 378, 391, 404, 417, 430, 443, 456, 469, 482, 495, 508, 521, 534, 547, 560, 573, 586, 599, 612, 625, 638, 651, 664, 677

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 29 2011

Keywords

• nonn
• easy

Comments

Partial sums give A051867. - Leo Tavares, Mar 19 2023

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A000012, A001477, A008594, A008595, A153080.

Cf. A051867.

Programs

Magma

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

Mathematica

Range[1, 1000, 13]
LinearRecurrence[{2,-1},{1,14},60] (* Harvey P. Dale, Apr 05 2014 *)

PARI

a(n)=13*n+1 \\ Charles R Greathouse IV, Jun 04 2020

SageMath

[13*n+1 for n in (0..60)] # G. C. Greubel, Sep 16 2022

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 11 2011

From Alejandro J. Becerra Jr., Jun 04 2020: (Start)

a(n) = 13*A001477(n) + A000012(n).

G.f.: (1 + 12*x)/(1 - x)^2. (End)

E.g.f.: (1+13*x)*exp(x). - G. C. Greubel, Sep 16 2022