A218828 - OEIS

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A218828

Reluctant sequence of reverse reluctant sequence A004736.

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

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OFFSET

1,3

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 A004736 is the reverse 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) = A004736(k) for every n.

As a linear array, the sequence is a(n) = (t1^2+3*t1+4)/2-n1, where n1=n-t(t+1)/2, 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:

1,2;

1,2,1;

1,2,1,3;