A112414 - OEIS

%I #16 Oct 30 2024 21:44:39

%S 7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,55,58,61,64,67,70,73,

%T 76,79,82,85,88,91,94,97,100,103,106,109,112,115,118,121,124,127,130,

%U 133,136,139,142,145,148,151,154,157,160,163,166,169,172,175,178,181,184

%N a(n) = 3*n + 7.

%C At least the first 2 million terms from a(1) on coincide with the corresponding terms of A086822(n+2). - _R. J. Mathar_, Aug 15 2008

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

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

%F From _Elmo R. Oliveira_, Oct 30 2024: (Start)

%F G.f.: (7 - 4*x)/(1 - x)^2.

%F E.g.f.: (7 + 3*x)*exp(x).

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

%F a(n) = A016933(n+2)/2 = A059845(n+1) - A059845(n). (End)

%t 3Range[0,70]+7 (* or *) LinearRecurrence[{2,-1},{7,10},70] (* _Harvey P. Dale_, May 12 2019 *)

%o (PARI) a(n)=3*n+7 \\ _Charles R Greathouse IV_, Jul 10 2016

%Y Cf. A016933, A059845.

%K easy,nonn,changed

%O 0,1

%A _Zerinvary Lajos_, Dec 09 2005

%E Better definition from _T. D. Noe_, Nov 30 2006