A072261 a(n) = 4*a(n-1) + 1, a(1)=7.

7, 29, 117, 469, 1877, 7509, 30037, 120149, 480597, 1922389, 7689557, 30758229, 123032917, 492131669, 1968526677, 7874106709, 31496426837, 125985707349, 503942829397, 2015771317589, 8063085270357, 32252341081429, 129009364325717, 516037457302869

Offset

1,1

Comments

These are the integers N which on application of the Collatz function yield the number 11. The Collatz function: if N is an odd number then (3N+1)/2^r yields a positive odd integer for some value of r (which in this case is 11).

These numbers reach 11 in Collatz function iteration after 2(n+1) steps and so end in 1 after exactly 2n+18 steps. - Lambert Klasen (lambert.klasen(AT)gmx.de), Nov 08 2004

Numbers whose binary representation is 111 together with n - 1 times 01. For example, a(4) = 469 = 111010101 (2). - Omar E. Pol, Nov 24 2012

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-4).

Index entries for sequences related to 3x+1 (or Collatz) problem

Formula

a(n) = (11*4^n - 2)/6 = 22*A002450(n-1) + 7. - Lambert Klasen (lambert.klasen(AT)gmx.de), Nov 08 2004

From Colin Barker, Oct 27 2019: (Start)

G.f.: x*(7 - 6*x) / ((1 - x)*(1 - 4*x)).

a(n) = 5*a(n-1) - 4*a(n-2) for n>2. (End)

E.g.f.: (-9 - 2*exp(x) + 11*exp(4*x))/6. - G. C. Greubel, Jan 14 2020

a(n) = a(n-1) + 11*2^(2*n-3), for n >= 2, with a(1) = 7. - Wolfdieter Lang, Aug 16 2021

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

Maple

seq(coeff(series(x*(7-6*x)/((1-x)*(1-4*x)), x, n+1), x, n), n = 1..25); # G. C. Greubel, Jan 14 2020

Mathematica

a[n_]:= 4a[n-1] +1; a[1]=7; Table[a[n], {n, 25}]
NestList[4#+1&, 7, 30] (* or *) LinearRecurrence[{5, -4}, {7, 29}, 30] (* Harvey P. Dale, Sep 04 2023 *)

Prog

(PARI) Vec(x*(7-6*x)/((1-x)*(1-4*x)) + O(x^25)) \\ Colin Barker, Oct 27 2019
(Magma) [(11*4^n -2)/6: n in [1..25]]; // G. C. Greubel, Jan 14 2020
(Sage) [(11*4^n -2)/6 for n in (1..25)] # G. C. Greubel, Jan 14 2020
(GAP) List([1..25], n-> (11*4^n -2)/6); # G. C. Greubel, Jan 14 2020

Crossrefs

Cf. A002450, A072197, A072257, A072258, A072259, A072260, A072262, A099730, A178415, A347834.

Sequence in context: A296646 A037094 A118171 * A066744 A037576 A327587

Adjacent sequences: A072258 A072259 A072260 * A072262 A072263 A072264

Keyword

nonn,easy

Author

N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002

Extensions

Edited and extended by Robert G. Wilson v, Jul 17 2002

More terms from Colin Barker, Oct 27 2019

Status

approved