A073188 n appears 1+[n/3] times.

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, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19

Offset

0,3

Comments

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)).

a(A001840(k) + j) = A001840(k), 0<=j < A008620(k). - Reinhard Zumkeller, Aug 01 2002

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..6900

Michael Somos, Sequences used for indexing triangular or square arrays

Formula

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

a(0)=0, then for n>=1 a(n)=1+a(n-1-floor(a(n-1)/3)). - Benoit Cloitre, May 08 2017

Mathematica

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

Prog

(PARI) a(n)=floor(sqrt(6*n+6)-3/2)
(PARI) t1(n)=floor(sqrt(6*n+6)-3/2) /* A073188 */
(PARI) t2(n)=(n-3*binomial(1+t1(n)\3, 2))%(t1(n)\3+1) /* A073189 */
(PARI) a(n)=if(n<1, 0, a(n-a(n-1)\3-1)+1) \\ Benoit Cloitre, May 08 2017
(Magma) [Floor(Sqrt(6*n+6)-3/2): n in [0..50]]; // G. C. Greubel, May 29 2018

Crossrefs

Cf. A073189.

Sequence in context: A303601 A031247 A062575 * A269225 A217713 A047740

Adjacent sequences: A073185 A073186 A073187 * A073189 A073190 A073191

Keyword

nonn

Author

Michael Somos, Jul 19 2002

Status

approved