A016993 a(n) = 7*n + 1.

1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85, 92, 99, 106, 113, 120, 127, 134, 141, 148, 155, 162, 169, 176, 183, 190, 197, 204, 211, 218, 225, 232, 239, 246, 253, 260, 267, 274, 281, 288, 295, 302, 309, 316, 323, 330, 337, 344, 351, 358, 365, 372, 379

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

For n > 3, also the number of (not necessarily maximal) cliques in the n-web graph. - Eric W. Weisstein, Nov 29 2017

The number of notes in a musical scale of n octaves. - Geoffrey Trueman Falk, Feb 16 2023

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• Tanya Khovanova, Recursive Sequences
• Eric Weisstein's World of Mathematics, Clique
• Eric Weisstein's World of Mathematics, Web Graph
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A093564 (column 1).

Cf. A131844, A008589.

Programs

Haskell

a016993 = (+ 1) . (* 7)
a016993_list = [1, 8 ..]  -- Reinhard Zumkeller, Jan 25 2013

Magma

[7*n+1: n in [0..60]]; // Vincenzo Librandi, May 28 2011

Maple

A016993:=n->7*n+1: seq(A016993(n), n=0..70); # Wesley Ivan Hurt, Nov 01 2014

Mathematica

7*Range[0, 55] + 1 (* Alonso del Arte, Oct 26 2014 *)
Table[7 n + 1, {n, 0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
LinearRecurrence[{2, -1}, {8, 15}, {0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
CoefficientList[Series[(1 + 6 x)/(-1 + x)^2, {x, 0, 20}], x] (* Eric W. Weisstein, Nov 29 2017 *)

PARI

a(n)=7*n+1 \\ Charles R Greathouse IV, Jul 10 2016

Formula

a(n) = 7*n + 1.

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

From Elmo R. Oliveira, Mar 07 2024: (Start)

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

E.g.f.: (1 + 7*x)*exp(x). (End)