A308196 Partial sums of A063808.

1, 5, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 181, 187, 193, 199, 205, 211, 217, 223, 229, 235, 241, 247, 253, 259, 265, 271, 277, 283, 289, 295, 301, 307, 313, 319, 325, 331, 337, 343, 349, 355

Offset

0,2

Comments

Growth series for Z as generated by {2,3}.

References

Avinoam Mann, How Groups Grow, London Mathematical Society Lecture Note Series, Vol. 335, Cambridge University Press, 2012; ISBN: 1107657504,9781107657502. See Example 6, page 3.

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = A271114(n) = A016921(n) = 6*n + 1 for n>=2. - R. J. Mathar, Jul 22 2021

From Elmo R. Oliveira, Dec 02 2025: (Start)

G.f.: (1 + 3*x + 4*x^2 - 2*x^3)/(x - 1)^2.

E.g.f.: (1 + 6*x)*exp(x) - 2*x.

a(n) = 2*a(n-1) - a(n-2) for n >= 4. (End)

Mathematica

Accumulate[PadRight[{1, 4, 8}, 100, 6]] (* Paolo Xausa, Nov 14 2023 *)

Crossrefs

Cf. A016921, A063808, A271114.

Sequence in context: A084442 A023270 A279765 * A287615 A129919 A045454

Adjacent sequences: A308193 A308194 A308195 * A308197 A308198 A308199

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 21 2019

Status

approved