A350052 Third part of the trisection of A017077: a(n) = 17 + 24*n.

17, 41, 65, 89, 113, 137, 161, 185, 209, 233, 257, 281, 305, 329, 353, 377, 401, 425, 449, 473, 497, 521, 545, 569, 593, 617, 641, 665, 689, 713, 737, 761, 785, 809, 833, 857, 881, 905, 929, 953, 977, 1001, 1025, 1049, 1073

Offset: 0

Author

Wolfdieter Lang, Dec 11 2021

Keywords

• nonn
• easy

Comments

The trisection of A017077 = {1 + 8*k}A103214%20=%20%7B1%20+%2024*n%7D">{k>=0} gives A103214 = {1 + 24*n}{n>=0}, 3*A017101 = {3*(3 + 8*n)}{n >= 0} and {a(n)}{n>=0}. These three sequences are congruent to 1 modulo 8 and to 1, 3, and 5 modulo 6, respectively.

Links

• Winston de Greef, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008606, A017077, 3*A017101, A103214.

Programs

Mathematica

24 * Range[0, 44] + 17 (* Amiram Eldar, Dec 18 2021 *)

PARI

a(n) = 17 + 24*n \\ Winston de Greef, Jan 28 2024

Formula

a(n) = 17 + 24*n = 17 + A008606(n), for n >= 0

a(n) = 2*a(n-1) - a(n-2), for n >= 1, with a(-1) = -7, a(0) = 17.

G.f.: (17 + 7*x)/(1-x)^2.

E.g.f.: (17 + 24*x)*exp(x).