A017653 a(n) = 12*n + 11.

11, 23, 35, 47, 59, 71, 83, 95, 107, 119, 131, 143, 155, 167, 179, 191, 203, 215, 227, 239, 251, 263, 275, 287, 299, 311, 323, 335, 347, 359, 371, 383, 395, 407, 419, 431, 443, 455, 467, 479, 491, 503, 515, 527, 539, 551, 563, 575, 587, 599, 611, 623, 635

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Or, with a different offset, 12*n - 1. In any case, numbers congruent to -1 (mod 12). - Alonso del Arte, May 29 2011

Numbers congruent to 2 (mod 3) and 3 (mod 4). - Bruno Berselli, Jul 06 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..3000
• John Elias, 60*n+55 Triangular Snowflakes.
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1000.
• Tanya Khovanova, Recursive Sequences.
• Leo Tavares, Illustration: Twin Hexagonal Frames.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A003215, A008594, A016969, A017533, A017545, A089911.

Subsequence of A072065.

Programs

Haskell

a017653 = (+ 11) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013

Magma

[12*n+11: n in [0..60]]; // Vincenzo Librandi, Jun 08 2011

Mathematica

Array[12*#+11&,100,0] (* Vladimir Joseph Stephan Orlovsky, Dec 14 2009 *)

PARI

a(n)=12*n+11

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 08 2011

G.f.: (11+x)/(1-x)^2. - Colin Barker, Feb 19 2012

A089911(2*a(n)) = 11. - Reinhard Zumkeller, Jul 05 2013

a(n) = 2*A003215(n+1) - 1 - 2*A003215(n). See Twin Hexagonal Frames illustration. - Leo Tavares, Aug 19 2021

From Elmo R. Oliveira, Apr 12 2025: (Start)

E.g.f.: exp(x)*(11 + 12*x).

a(n) = A016969(2*n+1). (End)