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Characteristic function of {3}.
16

%I #43 Jun 19 2024 09:16:05

%S 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,

%T 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,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Characteristic function of {3}.

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

%H J. S. Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_eq_g_index">Index of sequences counting connected k-regular simple graphs with girth exactly g</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

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

%F a(n) = [n = 3], where [ ] is the Iverson bracket. - _Wesley Ivan Hurt_, Dec 13 2013

%p A185013:=n->1-abs(signum(3-n)); seq(A185013(n), n=0..100); # _Wesley Ivan Hurt_, Dec 13 2013

%t Table[KroneckerDelta[n, 3], {n, 0, 100}] (* _Wesley Ivan Hurt_, Dec 13 2013 *)

%o (PARI) A185013(n)=n==3 \\ _M. F. Hasler_, Oct 30 2019

%o (Python)

%o def A185013(n): return int(n==3) # _Chai Wah Wu_, Feb 04 2022

%Y The Euler transformation of this sequence is A079978.

%Y 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).

%K nonn,easy

%O 0,1

%A _Jason Kimberley_, Oct 11 2011