A168313 Triangle read by rows, retain 1's as rightmost diagonal of A101688 and replace all other 1's with 2's.

1, 0, 1, 0, 2, 1, 0, 0, 2, 1, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1

Offset

1,5

Comments

Row sums = odd integers repeated: (1, 1, 3, 3, 5, 5,...).

Eigensequence of the triangle = A168314: (1, 1, 3, 5, 13, 29, 71, 165, 401,...).

Links

Table of n, a(n) for n=1..66.

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

Formula

Triangle read by rows, retain 1's as rightmost diagonal of A101688 and replace all other 1's with 2's.

From Boris Putievskiy, Jan 09 2013: (Start)

a(n) = 2*A101688(n)-A023531(n).

a(n) = 2*floor((2*A002260(n)+1)/(A003056(n)+3))*A002260(n)-A023531(n).

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

Example

First few rows of the triangle =
1;
0, 1;
0, 2, 1;
0, 0, 2, 1;
0, 0, 2, 2, 1;
0, 0, 0, 2, 2, 1;
0, 0, 0, 2, 2, 2, 1;
0, 0, 0, 0, 2, 2, 2, 1;
0, 0, 0, 0, 2, 2, 2, 2, 1;
0, 0, 0, 0, 0, 2, 2, 2, 2, 1;
0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1;
0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 1;
...

Mathematica

rows = 11;
A = Array[Which[#1 == 1, 1, #1 <= #2, 2, True, 0]&, {rows, rows}];
Table[A[[i-j+1, j]], {i, 1, rows}, {j, 1, i}] // Flatten (* Jean-François Alcover, Aug 08 2018 *)

Crossrefs

Cf. A101688, A168314, A168315

Sequence in context: A226862 A226864 A257399 * A072575 A025872 A280125

Adjacent sequences: A168310 A168311 A168312 * A168314 A168315 A168316

Keyword

nonn,tabl

Author

Gary W. Adamson, Nov 22 2009

Status

approved