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A210535 Second inverse function (numbers of columns) for pairing function A209293. 2
1, 2, 1, 2, 3, 1, 2, 4, 3, 1, 2, 4, 5, 3, 1, 2, 4, 6, 5, 3, 1, 2, 4, 6, 7, 5, 3, 1, 2, 4, 6, 8, 7, 5, 3, 1, 2, 4, 6, 8, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 11, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 12, 11, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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

Eric W. Weisstein, MathWorld: Pairing functions

FORMULA

a(n) = 2*A200260(n)-A101688(n)*(4*A002260(n)-2*A003056(n)-3).

a(n) = 2*i-v*(4*i-2*t-3), where t = floor((-1+sqrt(8*n-7))/2), i = n-t*(t+1)/2, v = floor((2*n+1-t*(t+1))/(t+3)).

EXAMPLE

The start of the sequence as triangle array read by rows:

1;

2,1;

2,3,1;

2,4,3,1;

2,4,5,3,1;

2,4,6,5,3,1;

2,4,6,7,5,3,1;

2,4,6,8,7,5,3,1;

. . .

Row number r contains permutation numbers from 1 to r:

2,4,6,...2*floor(r/2),2*floor(r/2)-1,2*floor(r/2)-3,...3,1.

PROG

(Python)

t=int((math.sqrt(8*n-7)-1)/2)

i=n-t*(t+1)/2

v=int((2*n+1-t*(t+1))/(t+3))

result=2*i-v*(4*i-2*t-3)

CROSSREFS

Cf. A209293, A200260, A101688, A003056, A220073.

Sequence in context: A265692 A194976 A195082 * A194983 A195073 A194987

Adjacent sequences:  A210532 A210533 A210534 * A210536 A210537 A210538

KEYWORD

nonn

AUTHOR

Boris Putievskiy, Jan 28 2013

STATUS

approved

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Last modified September 21 16:31 EDT 2021. Contains 347598 sequences. (Running on oeis4.)