A330246 a(n) = 4^(n+1) + (4^n-1)/3.

4, 17, 69, 277, 1109, 4437, 17749, 70997, 283989, 1135957, 4543829, 18175317, 72701269, 290805077, 1163220309, 4652881237, 18611524949, 74446099797, 297784399189, 1191137596757, 4764550387029, 19058201548117, 76232806192469, 304931224769877, 1219724899079509

Offset: 0

Author

Vincenzo Librandi, Jan 09 2020

Keywords

• nonn
• easy

Comments

After 4, these numbers are the third column of the rectangular array in A238475.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-4).
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Similar to A272743.

Cf. A000302, A002450, A052909, A178415, A237930, A238475, A347834.

Together with 1: first bisection of A136326.

Programs

Magma

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

Mathematica

Table[(4^(n + 1) + (4^n - 1) / 3), {n, 0, 30}]

Formula

G.f.: (4 - 3*x) / ((1 - x)*(1 - 4*x)).

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

a(n) = 4*a(n-1) + 1 for n > 0.

a(n) = (13*4^n -1)/3, for n >= 0. - Wolfdieter Lang, Sep 16 2021

a(n) = A178415(5, n) = A347834(7, n-1), arrays, for n >= 1. - Wolfdieter Lang, Nov 29 2021