A220464 Reverse reluctant sequence of reluctant sequence A002260.

1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 3, 2, 1, 2, 1, 1, 1, 3, 2, 1, 2, 1, 1, 2, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 3, 2, 1, 2, 1, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 2, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 4, 3, 2, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 5, 4, 3, 2, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 1, 5, 4, 3

Offset

1,4

Comments

Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A.

Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order.

Sequence A002260 is the reluctant sequence of sequence 1,2,3,... (A000027).

Links

Boris Putievskiy, Rows n = 1..140 of triangle, flattened

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Formula

T(n,k) = A002260(n-k+1).

As a linear array, the sequence is a(n) = n1-t1*(t1+1)/2, where n1=(t*t+3*t+4)/2-n, t1=floor[(-1+sqrt(8*n1-7))/2], t=floor[(-1+sqrt(8*n-7))/2].

Example

The start of the sequence as triangle array T(n,k) is:
  1;
  1,1;
  2,1,1;
  1,2,1,1;
  2,1,2,1,1;
  3,2,1,2,1,1;
  ...

Prog

(Python)
t=int((math.sqrt(8*n-7) - 1)/ 2)
n1=(t*t+3*t+4)/2-n
t1=int((math.sqrt(8*n1-7) - 1)/ 2)
m=n1-t1*(t1+1)/2

Crossrefs

Cf. A002260, A004736, A220280.

Sequence in context: A105141 A103961 A012257 * A215975 A071891 A359306

Adjacent sequences: A220461 A220462 A220463 * A220465 A220466 A220467

Keyword

easy,nonn,tabl

Author

Boris Putievskiy, Dec 15 2012

Status

approved