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A168313 Triangle read by rows, retain 1's as rightmost diagonal of A101688 and replace all other 1's with 2's. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 11 00:32 EDT 2020. Contains 336403 sequences. (Running on oeis4.)