A351782 a(n) = n-2 if n is a multiple of 4, a(n) = n-1 otherwise.

0, 1, 2, 2, 4, 5, 6, 6, 8, 9, 10, 10, 12, 13, 14, 14, 16, 17, 18, 18, 20, 21, 22, 22, 24, 25, 26, 26, 28, 29, 30, 30, 32, 33, 34, 34, 36, 37, 38, 38, 40, 41, 42, 42, 44, 45, 46, 46, 48, 49, 50, 50, 52, 53, 54, 54, 56, 57, 58, 58, 60, 61, 62, 62, 64, 65, 66, 66, 68, 69

Offset

1,3

Comments

a(n) is the rank of the walk matrix of the Dynkin graph Dn, a tree obtained from the path of order n-1 by adding a pendant edge at the second vertex. see Wang et al.

Links

Table of n, a(n) for n=1..70.

Wei Wang, Chuanming Wang, and Songlin Guo, On the walk matrix of the Dynkin graph Dn, arXiv:2202.13279 [math.CO], 2022.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

From Wesley Ivan Hurt, Mar 03 2022: (Start)

a(n) = n - 2 + sign(n mod 4).

a(n) = n - 1 - A121262(n). (End)

Mathematica

a[n_] := If[Divisible[n, 4], n - 2, n - 1]; Array[a, 70] (* Amiram Eldar, Mar 03 2022 *)

Prog

(PARI) a(n) = if (n%4, n-1, n-2);
(Python)
def A351782(n): return n - 1 - int(n % 4 == 0) # Chai Wah Wu, Mar 04 2022

Crossrefs

Cf. A121262.

Sequence in context: A263433 A147806 A338228 * A064574 A059015 A325108

Adjacent sequences: A351779 A351780 A351781 * A351783 A351784 A351785

Keyword

nonn,easy

Author

Michel Marcus, Mar 03 2022

Status

approved