A347837 a(n) = 32*(n + floor(n/3)) - 11; third column of A347834.

21, 53, 117, 149, 181, 245, 277, 309, 373, 405, 437, 501, 533, 565, 629, 661, 693, 757, 789, 821, 885, 917, 949, 1013, 1045, 1077, 1141, 1173, 1205, 1269, 1301, 1333, 1397, 1429, 1461, 1525, 1557, 1589, 1653, 1685

Offset: 1

Author

Wolfdieter Lang, Oct 07 2021

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

Cf. A047529 (first column), A178415, A265667, A319451, A347834, A347836 (second column).

Programs

Magma

[32*(n + Floor(n/3)) - 11 : n in [1..60]]; // Wesley Ivan Hurt, Oct 10 2021

Maple

seq(32*(n + floor(n/3)) - 11, n=1..40); # Peter Luschny, Oct 10 2021

Mathematica

A347837[n_] := 32*(n + Floor[n/3]) - 11; Array[A347837, 50] (* or *)
LinearRecurrence[{1, 0, 1, -1}, {21, 53, 117, 149}, 50] (* Paolo Xausa, Feb 27 2024 *)

Formula

a(n) = A347834(n, 2) = A178415(A265667(n), 3), for n >= 1.

a(n) = ((3*A047529(n) + 1)*16 - 1)/3 = ((3*(n + floor(n/3)) - 1)*32 - 1)/3 = ((A319451(n) - 1)*32 - 1)/3, for n >= 1.

O.g.f.: G(x) = (-11 + 32*x + 32*x^2 + 75*x^3)/((1 - x)*(1 - x^3)), with a(0) = -11.