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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
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, 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
KEYWORD
easy,nonn,tabl
AUTHOR
Boris Putievskiy, Dec 15 2012
STATUS
approved