A291557 a(n) = 23*2^n - 1.

22, 45, 91, 183, 367, 735, 1471, 2943, 5887, 11775, 23551, 47103, 94207, 188415, 376831, 753663, 1507327, 3014655, 6029311, 12058623, 24117247, 48234495, 96468991, 192937983, 385875967, 771751935, 1543503871, 3087007743, 6174015487, 12348030975, 24696061951, 49392123903, 98784247807, 197568495615, 395136991231, 790273982463, 1580547964927

Offset: 0

Author

Enrique Navarrete, Aug 26 2017

Keywords

• nonn
• easy

Comments

An easy description is: starting from a(0)=22, a(n)=number of integers to be skipped to get a(n+1); i.e., from a(0)=22, skip 22 integers to get a(1)=45; then skip 45 integers to get a(2)=91, etc.

Note that if the initial condition is a(0)=0, a(n)=A000225; if a(0)=2, a(n)=A083329; if a(0)=4, a(n)=A153894, etc.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..3317
• Gennady Eremin, Partitioning the set of natural numbers into Mersenne trees and into arithmetic progressions; Natural Matrix and Linnik's constant, arXiv:2405.16143 [math.CO], 2024. See pp. 3-5, 14.
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A000225, A083329, A153894.

Programs

Maple

A291557:=n->23*2^n-1: seq(A291557(n), n=0..50); # Wesley Ivan Hurt, Oct 05 2017

Mathematica

23*2^Range[0,40]-1 (* or *) LinearRecurrence[{3,-2},{22,45},40] (* Harvey P. Dale, Jul 20 2018 *)

PARI

a(n) = 23*2^n - 1; \\ Altug Alkan, Mar 04 2018

Formula

From Chai Wah Wu, Mar 04 2018: (Start)

a(n) = 3*a(n-1) - 2*a(n-2) for n > 1.

G.f.: (22 - 21*x)/((1 - x)*(1 - 2*x)). (End)