A017137 a(n) = 8*n + 6.

6, 14, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94, 102, 110, 118, 126, 134, 142, 150, 158, 166, 174, 182, 190, 198, 206, 214, 222, 230, 238, 246, 254, 262, 270, 278, 286, 294, 302, 310, 318, 326, 334, 342, 350, 358, 366, 374, 382, 390, 398, 406, 414, 422, 430

Offset: 0

Author

N. J. A. Sloane, Dec 11 1996

Keywords

• nonn
• easy

Comments

First differences of A002943. - Aaron David Fairbanks, May 13 2014

Examples

			G.f. = 6 + 14*x + 22*x^2 + 30*x^3 + 38*x^4 + 46*x^5 + 54*x^6 + 62*x^7 + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A000290, A002943, A004767, A004770, A008590, A017101, A017113, A017245, A156676.

Cf. A016825, A017629, A047595 (complement), A089911.

Programs

Haskell

a017137 = (+ 6) . (* 8)  -- Reinhard Zumkeller, Jul 05 2013

Magma

[8*n+6: n in [0..60]]; // Vincenzo Librandi, Jun 07 2011

Maple

A017137:=n->8*n+6; seq(A017137(n), n=0..50); # Wesley Ivan Hurt, May 13 2014

Mathematica

Range[6, 1000, 8] (* Vladimir Joseph Stephan Orlovsky, May 27 2011 *)
8Range[0,60]+6 (* or *) LinearRecurrence[{2,-1},{6,14},60] (* Harvey P. Dale, Nov 14 2021 *)

PARI

a(n) = 8*n+6; \\ Michel Marcus, Sep 17 2015

PARI

Vec((6+2*x)/(1-x)^2 + O(x^100)) \\ Altug Alkan, Oct 23 2015

Formula

a(n) = 2*A004767(n) = A000290(A017245(n)) - A156676(n+1). - Reinhard Zumkeller, Jul 13 2010

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 07 2011

A089911(3*a(n)) = 4. - Reinhard Zumkeller, Jul 05 2013

From Michael Somos, May 15 2014: (Start)

G.f.: (6 + 2*x)/(1 - x)^2.

E.g.f.: (6 + 8*x)*exp(x). (End)

Sum_{n>=0} (-1)^n/a(n) = (Pi + log(3-2*sqrt(2)))/(8*sqrt(2)). - Amiram Eldar, Dec 11 2021

a(n) = A016825(2*n+1). - Elmo R. Oliveira, Apr 12 2025