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

Author

Boris Putievskiy, Dec 15 2012

Keywords

• easy
• nonn
• tabl

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).

Examples

			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;
  ...
		

Links

• Boris Putievskiy, Rows n = 1..140 of triangle, flattened
• Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Crossrefs

Cf. A002260, A004736, A220280.

Programs

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

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].