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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
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
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
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Nov 22 2009
STATUS
approved