A392083 a(n) = 2*a(n-1) + 2^(n+1) - 1, a(0) = 0.

0, 3, 13, 41, 113, 289, 705, 1665, 3841, 8705, 19457, 43009, 94209, 204801, 442369, 950273, 2031617, 4325377, 9175041, 19398657, 40894465, 85983233, 180355073, 377487361, 788529153, 1644167169, 3422552065, 7113539585, 14763950081, 30601641985, 63350767617

Offset

0,2

Comments

A recurrence relation that occurs in A391958.

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Formula

a(n) = A391958(2^n).

From Stefano Spezia, Dec 30 2025: (Start)

a(n) = n*2^(n+1) - 2^n + 1.

G.f.: x*(3 - 2*x)/((1 - 2*x)^2*(1 - x)).

E.g.f.: exp(x)*(1 + exp(x)*(4*x - 1)). (End)

Mathematica

a[n_] := n*2^(n+1) - 2^n + 1; Array[a, 31, 0] (* Amiram Eldar, Dec 30 2025 *)

Prog

(Python)
def A392083(n):
    if n == 0: return 0
    else: return 2*A392083(n-1) + 2**(n+1) - 1

Crossrefs

Cf. A391958.

Sequence in context: A309139 A049167 A241527 * A234387 A173867 A121162

Adjacent sequences: A392080 A392081 A392082 * A392084 A392085 A392086

Keyword

nonn,easy

Author

A.H.M. Smeets, Dec 30 2025

Status

approved