A017605 a(n) = 12*n + 7.

7, 19, 31, 43, 55, 67, 79, 91, 103, 115, 127, 139, 151, 163, 175, 187, 199, 211, 223, 235, 247, 259, 271, 283, 295, 307, 319, 331, 343, 355, 367, 379, 391, 403, 415, 427, 439, 451, 463, 475, 487, 499, 511, 523, 535, 547, 559, 571, 583, 595, 607, 619, 631

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Tanya Khovanova, Recursive Sequences
• Leo Tavares, Illustration: Hexagonal Wheels
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008594, A016921, A017533, A017545, A068229.

Cf. A000217, A003215, A049453, A142241.

Programs

Mathematica

12*Range[0,200] + 7 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

PARI

a(n)=12*n+7 \\ Charles R Greathouse IV, Jul 10 2016

Sage

[i+7 for i in range(525) if gcd(i,12) == 12] # Zerinvary Lajos, May 21 2009

Formula

a(n) = 2*(12*n+1) - a(n-1) = 2*a(n-1) - a(n-2) with a(0) = 7, a(1) = 19. - Vincenzo Librandi, Nov 19 2010

a(n) = (n+1)*A016921(n+1) - n*A016921(n). - Bruno Berselli, Jan 18 2013

a(n) = A003215(n+1) - 6*A000217(n-1). - Leo Tavares, Jul 25 2021

From Elmo R. Oliveira, Apr 02 2024: (Start)

G.f.: (7+5*x)/(1-x)^2.

E.g.f.: exp(x)*(7 + 12*x).

a(n) = A049453(n+1) - A049453(n) = A142241(n)/2. (End)