A154609 a(n) = 13*n + 5.

5, 18, 31, 44, 57, 70, 83, 96, 109, 122, 135, 148, 161, 174, 187, 200, 213, 226, 239, 252, 265, 278, 291, 304, 317, 330, 343, 356, 369, 382, 395, 408, 421, 434, 447, 460, 473, 486, 499, 512, 525, 538, 551, 564, 577, 590, 603, 616, 629, 642, 655, 668, 681, 694

Offset: 0

Author

Vincenzo Librandi, Jan 15 2009

Keywords

• nonn
• easy

Comments

Any square mod 13 is one of 0, 1, 3, 4, 9, 10 or 12 (A010376) but not 5, for this reason there are no squares in sequence. - Bruno Berselli, Feb 19 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A010376,

Sequences of the form 13*n+q: A008595 (q=0), A190991 (q=1), A153080 (q=2), A127547 (q=4), this sequence (q=5), A186113 (q=6), A269044 (q=7), A269100 (q=11).

Programs

Magma

I:=[5, 18]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 26 2012

Mathematica

Range[5, 1000, 13] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)
CoefficientList[Series[(8 x + 5)/(1 - x)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Feb 26 2012 *)

PARI

a(n)=13*n+5 \\ Charles R Greathouse IV, Dec 28 2011

SageMath

[13*n+5 for n in range(61)] # G. C. Greubel, May 31 2024

Formula

From Vincenzo Librandi, Feb 26 2012: (Start)

G.f.: (5+8*x)/(1-x)^2.

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

E.g.f.: (5 + 13*x)*exp(x). - G. C. Greubel, May 31 2024