A206374 - OEIS

%I #62 Sep 08 2022 08:46:01

%S 2,9,37,149,597,2389,9557,38229,152917,611669,2446677,9786709,

%T 39146837,156587349,626349397,2505397589,10021590357,40086361429,

%U 160345445717,641381782869,2565527131477,10262108525909,41048434103637,164193736414549,656774945658197

%N a(n) = (7*4^n - 1)/3.

%C First bisection of A062092 and A081253, second bisection of A097163. - _Bruno Berselli_, Feb 12 2012

%C Except a(0)=2, this is the 3rd row of table A178415. - _Michel Marcus_, Apr 13 2015

%H Vincenzo Librandi, <a href="/A206374/b206374.txt">Table of n, a(n) for n = 0..1000</a>

%H Mike Warburton, <a href="https://arxiv.org/abs/1901.10565">Ulam-Warburton Automaton - Counting Cells with Quadratics</a>, arXiv:1901.10565 [math.CO], 2019. See Table 1.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).

%F G.f.: (2-x)/(1-5*x+4*x^2). - _Bruno Berselli_, Feb 12 2012

%F a(n) = A083597(n)+1. - _Bruno Berselli_, Feb 12 2012

%F a(n) = 4*a(n-1)+1 for n>0, a(0)=2. - _Bruno Berselli_, Oct 22 2015

%F a(n) = 7*A002450(n) + 2. - _Yosu Yurramendi_, Jan 24 2017

%F A006666(a(n)) = 2*n+11 for n > 0. - _Juan Miguel Barga Pérez_, Jun 18 2020

%F a(n) = 5*a(n-1) - 4*a(n-2) for n >= 2. - _Wesley Ivan Hurt_, Jun 30 2020

%F a(n) = A178415(3, n) = A347834(4, n-1), arrays, for n >= 1.- _Wolfdieter Lang_, Nov 29 2021

%t Table[(7(4^n) - 1)/3, {n, 0, 24}] (* _Alonso del Arte_, Feb 11 2012 *)

%t CoefficientList[Series[(2-x)/(1-5*x+4*x^2),{x,0,30}],x] (* or *) LinearRecurrence[{5,-4},{2,9},30] (* _Vincenzo Librandi_, Mar 20 2012 *)

%o (Magma) [(7*4^n-1)/3 : n in [0..30]];

%o (PARI) vector(20,n,(7*4^(n-1)-1)/3) \\ _Derek Orr_, Apr 12 2015

%Y Cf. A002450, A006666, A072197; A002042 (first differences), A178415, A347834.

%K nonn,easy

%O 0,1

%A _Brad Clardy_, Feb 07 2012