A206374 a(n) = (7*4^n - 1)/3.

2, 9, 37, 149, 597, 2389, 9557, 38229, 152917, 611669, 2446677, 9786709, 39146837, 156587349, 626349397, 2505397589, 10021590357, 40086361429, 160345445717, 641381782869, 2565527131477, 10262108525909, 41048434103637, 164193736414549, 656774945658197

Offset: 0

Author

Brad Clardy, Feb 07 2012

Keywords

• nonn
• easy

Comments

First bisection of A062092 and A081253, second bisection of A097163. - Bruno Berselli, Feb 12 2012

Except a(0)=2, this is the 3rd row of table A178415. - Michel Marcus, Apr 13 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Mike Warburton, Ulam-Warburton Automaton - Counting Cells with Quadratics, arXiv:1901.10565 [math.CO], 2019. See Table 1.
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

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

Programs

Magma

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

Mathematica

Table[(7(4^n) - 1)/3, {n, 0, 24}] (* Alonso del Arte, Feb 11 2012 *)
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 *)

PARI

vector(20,n,(7*4^(n-1)-1)/3) \\ Derek Orr, Apr 12 2015

Formula

G.f.: (2-x)/(1-5*x+4*x^2). - Bruno Berselli, Feb 12 2012

a(n) = A083597(n)+1. - Bruno Berselli, Feb 12 2012

a(n) = 4*a(n-1)+1 for n>0, a(0)=2. - Bruno Berselli, Oct 22 2015

a(n) = 7*A002450(n) + 2. - Yosu Yurramendi, Jan 24 2017

A006666(a(n)) = 2*n+11 for n > 0. - Juan Miguel Barga Pérez, Jun 18 2020

a(n) = 5*a(n-1) - 4*a(n-2) for n >= 2. - Wesley Ivan Hurt, Jun 30 2020

a(n) = A178415(3, n) = A347834(4, n-1), arrays, for n >= 1.- Wolfdieter Lang, Nov 29 2021