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a(n) = 7*n + 1.
32

%I #64 Mar 08 2024 17:27:29

%S 1,8,15,22,29,36,43,50,57,64,71,78,85,92,99,106,113,120,127,134,141,

%T 148,155,162,169,176,183,190,197,204,211,218,225,232,239,246,253,260,

%U 267,274,281,288,295,302,309,316,323,330,337,344,351,358,365,372,379

%N a(n) = 7*n + 1.

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

%C The number of notes in a musical scale of n octaves. - _Geoffrey Trueman Falk_, Feb 16 2023

%H Vincenzo Librandi, <a href="/A016993/b016993.txt">Table of n, a(n) for n = 0..5000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Clique.html">Clique</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WebGraph.html">Web Graph</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 7*n + 1.

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

%F From _Elmo R. Oliveira_, Mar 07 2024: (Start)

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

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

%p A016993:=n->7*n+1: seq(A016993(n), n=0..70); # _Wesley Ivan Hurt_, Nov 01 2014

%t 7*Range[0, 55] + 1 (* _Alonso del Arte_, Oct 26 2014 *)

%t Table[7 n + 1, {n, 0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)

%t LinearRecurrence[{2, -1}, {8, 15}, {0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)

%t CoefficientList[Series[(1 + 6 x)/(-1 + x)^2, {x, 0, 20}], x] (* _Eric W. Weisstein_, Nov 29 2017 *)

%o (Magma) [7*n+1: n in [0..60]]; // _Vincenzo Librandi_, May 28 2011

%o (Haskell)

%o a016993 = (+ 1) . (* 7)

%o a016993_list = [1, 8 ..] -- _Reinhard Zumkeller_, Jan 25 2013

%o (PARI) a(n)=7*n+1 \\ _Charles R Greathouse IV_, Jul 10 2016

%Y Cf. A093564 (column 1).

%Y Cf. A131844, A008589.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_