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A220464 Reverse reluctant sequence of reluctant sequence A002260. 1
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 (list; graph; refs; listen; history; text; internal format)
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]

FORMULA

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;

. . .

T(n,k)=A002260(n-k+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: A293811 A105141 A103961 * A215975 A071891 A046072

Adjacent sequences:  A220461 A220462 A220463 * A220465 A220466 A220467

KEYWORD

easy,nonn,tabf

AUTHOR

Boris Putievskiy, Dec 15 2012

STATUS

approved

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Last modified May 19 13:02 EDT 2019. Contains 323393 sequences. (Running on oeis4.)