A350051 Part three of the trisection of A017101: a(n) = 19 + 24*n.

19, 43, 67, 91, 115, 139, 163, 187, 211, 235, 259, 283, 307, 331, 355, 379, 403, 427, 451, 475, 499, 523, 547, 571, 595, 619, 643, 667, 691, 715, 739, 763, 787, 811, 835, 859, 883, 907, 931, 955, 979, 1003, 1027, 1051, 1075

Offset: 0

Author

Wolfdieter Lang, Dec 11 2021

Keywords

• nonn
• easy

Comments

The trisection of A017101 = {3 + 8*k}A017077%20=%20%7B3*(1%20+%2012*n)%7D">{k>=0} gives 3*A017077 = {3*(1 + 12*n)}{n>=0}, {A348845(n)}{n >= 0} and {a(n)}{n>=0}. These three sequences are congruent to 3 modulo 8 and to 3, 5, and 1 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, 3*A017077, A017101, A348845.

Programs

Mathematica

24 * Range[0, 44] + 19 (* Amiram Eldar, Dec 18 2021 *)

PARI

a(n) = 19 + 24*n \\ Winston de Greef, Jan 28 2024

Formula

a(n) = 19 + 24*n = 19 + A008606(n), for n >= 0

a(n) = 2*a(n-1) - a(n-2), for n >= 1, with a(-1) = -5, a(0) = 19.

G.f.: (19 + 5*x)/(1-x)^2.

E.g.f.: (19 + 24*x)*exp(x).