A185013 Characteristic function of {3}.

0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Jason Kimberley, Oct 11 2011

Keywords

• nonn
• easy

Comments

Number of connected 2-regular (simple) graphs with girth exactly 3.

Links

• J. S. Kimberley, Index of sequences counting connected k-regular simple graphs with girth exactly g
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

The Euler transformation of this sequence is A079978.

Characteristic function of {g}: A000007 (g=0), A063524 (g=1), A185012 (g=2), this sequence (g=3), A185014 (g=4), A185015 (g=5), A185016 (g=6), A185017 (g=7).

Programs

Maple

A185013:=n->1-abs(signum(3-n)); seq(A185013(n), n=0..100); # Wesley Ivan Hurt, Dec 13 2013

Mathematica

Table[KroneckerDelta[n, 3], {n, 0, 100}] (* Wesley Ivan Hurt, Dec 13 2013 *)

PARI

A185013(n)=n==3 \\ M. F. Hasler, Oct 30 2019

Python

def A185013(n): return int(n==3) # Chai Wah Wu, Feb 04 2022

Formula

a(n) = A179184(n) - A185114(n).

a(n) = [n = 3], where [ ] is the Iverson bracket. - Wesley Ivan Hurt, Dec 13 2013