A073188 - OEIS

%I #26 Sep 08 2022 08:45:06

%S 0,1,2,3,3,4,4,5,5,6,6,6,7,7,7,8,8,8,9,9,9,9,10,10,10,10,11,11,11,11,

%T 12,12,12,12,12,13,13,13,13,13,14,14,14,14,14,15,15,15,15,15,15,16,16,

%U 16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,19,19,19,19,19,19

%N n appears 1+[n/3] times.

%C The PARI functions t1, t2 can be used to read a triangular array T(n,k) (n >= 0, 0 <= k <= floor(n/3)) by rows from left to right: n -> T(t1(n), t2(n)).

%C a(A001840(k) + j) = A001840(k), 0<=j < A008620(k). - _Reinhard Zumkeller_, Aug 01 2002

%H Vincenzo Librandi, <a href="/A073188/b073188.txt">Table of n, a(n) for n = 0..6900</a>

%H Michael Somos, <a href="/A073189/a073189.txt">Sequences used for indexing triangular or square arrays</a>

%F a(n) = floor(sqrt(6n+6)-3/2).

%F a(0)=0, then for n>=1 a(n)=1+a(n-1-floor(a(n-1)/3)). - _Benoit Cloitre_, May 08 2017

%t Flatten[Table[c=1+Floor[n/3];Table[n,{c}],{n,0,20}]] (* _Harvey P. Dale_, Nov 01 2013 *)

%o (PARI) a(n)=floor(sqrt(6*n+6)-3/2)

%o (PARI) t1(n)=floor(sqrt(6*n+6)-3/2) /* A073188 */

%o (PARI) t2(n)=(n-3*binomial(1+t1(n)\3,2))%(t1(n)\3+1) /* A073189 */

%o (PARI) a(n)=if(n<1,0,a(n-a(n-1)\3-1)+1) \\ _Benoit Cloitre_, May 08 2017

%o (Magma) [Floor(Sqrt(6*n+6)-3/2): n in [0..50]]; // _G. C. Greubel_, May 29 2018

%Y Cf. A073189.

%K nonn

%O 0,3

%A _Michael Somos_, Jul 19 2002