login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210536 T(n,k) = 3*n + (k-1) mod 3 - 2; n , k > 0, read by antidiagonals. 0
1, 2, 4, 3, 5, 7, 1, 6, 8, 10, 2, 4, 9, 11, 13, 3, 5, 7, 12, 14, 16, 1, 6, 8, 10, 15, 17, 19, 2, 4, 9, 11, 13, 18, 20, 22, 3, 5, 7, 12, 14, 16, 21, 23, 25, 1, 6, 8, 10, 15, 17, 19, 24, 26, 28, 2, 4, 9, 11, 13, 18, 20, 22, 27, 29, 2, 9, 31, 3, 5, 7, 12, 14, 16 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Columns 3*k-2 are A016777,

Columns 3*k-1 are A016789,

Columns 3*k   are A008585.

Rows 1 is A010882.

LINKS

Table of n, a(n) for n=1..74.

Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.

FORMULA

a(n) = 3*A002260(n) + (A004736(n) - 1) mod 3 - 2. a(n) = 3*i + (j-1) mod 3 - 2, where i = n-t*(t+1)/2, j = (t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2).

EXAMPLE

The start of the sequence as table:

1....2...3...1...2...3...1...2...3...

4....5...6...4...5...6...4...5...6...

7....8...9...7...8...9...7...8...9...

10..11..12..10..11..12..10..11..12...

13..14..15..13..14..15..13..14..15...

16..17..18..16..17..18..16..17..18...

19..20..21..19..20..21..19..20..21...

22..23..24..22..23..24..22..23..24...

25..26..27..25..26..27..25..26..27...

. . .

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

1;

2,4;

3,5,7;

1,6,8,10;

2,4,9,11,13;

3,5,7,12,14,16;

1,6,8,10,15,17,19;

2,4,9,11,13,18,20,22;

3,5,7,12,14,16,21,23,25;

. . .

PROG

(Python)

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

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

j=(t*t+3*t+4)/2-n

result=3*i + (j-1) % 3 - 2

CROSSREFS

Cf. A016777, A016789, A008585, A010882, A002260, A004736, A131225.

Sequence in context: A102568 A338834 A338835 * A102767 A336640 A258238

Adjacent sequences:  A210533 A210534 A210535 * A210537 A210538 A210539

KEYWORD

nonn,tabl

AUTHOR

Boris Putievskiy, Jan 29 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 21 18:08 EST 2022. Contains 350479 sequences. (Running on oeis4.)