A147587 a(n) = 14*n + 7.

7, 21, 35, 49, 63, 77, 91, 105, 119, 133, 147, 161, 175, 189, 203, 217, 231, 245, 259, 273, 287, 301, 315, 329, 343, 357, 371, 385, 399, 413, 427, 441, 455, 469, 483, 497, 511, 525, 539, 553, 567, 581, 595, 609, 623, 637, 651, 665, 679, 693, 707, 721, 735

Offset: 0

Author

Paul Curtz, Nov 08 2008

Keywords

• nonn
• easy

Comments

a(n+3) = 14*n + 49 is the sum of seven consecutive odd numbers starting with 2*n+1. - Wesley Ivan Hurt, Apr 11 2015

Numbers k such that 3^k + 1 is divisible by 547. - Bruno Berselli, Aug 22 2018

Sum of the numbers from 2*(n-1) to 2*(n+2). - Bruno Berselli, Oct 25 2018

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A005408, A008596, A131877, A132355, A132744.

Programs

Magma

[14*n+7 : n in [0..100]]; // Wesley Ivan Hurt, Apr 11 2015

Maple

A147587:=n->14*n+7: seq(A147587(n), n=0..100); # Wesley Ivan Hurt, Apr 11 2015

Mathematica

Range[7, 1000, 14] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)

PARI

a(n)=14*n+7 \\ Charles R Greathouse IV, Oct 16 2015

Formula

a(n) = a(n-1) + 14.

a(n) = A132355(2*n+2) - A132355(2*n+1) = 7*A005408(n).

a(n) = 28*n - a(n-1) for n>0, a(0)=7. - Vincenzo Librandi, Nov 24 2010

From Wesley Ivan Hurt, Apr 11 2015: (Start)

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

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

Sum_{n>=0} (-1)^n/a(n) = Pi/28 (A132744). - Amiram Eldar, Dec 13 2021

From Amiram Eldar, Nov 25 2024: (Start)

Product_{n>=0} (1 - (-1)^n/a(n)) = sqrt(2)*sin(3*Pi/14).

Product_{n>=0} (1 + (-1)^n/a(n)) = sqrt(2)*cos(3*Pi/14). (End)

a(n) = (n+4)^2 - (n-3)^2. - Alexander Yutkin, Mar 16 2025

E.g.f.: 7*exp(x)*(1 + 2*x). - Stefano Spezia, Mar 18 2025

Extensions

More terms from Vincenzo Librandi, Oct 23 2009