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%I #17 Feb 15 2022 09:53:55

%S 1,0,2,1,0,3,0,2,0,4,1,0,3,0,5,0,2,0,4,0,6,1,0,3,0,5,0,7,0,2,0,4,0,6,

%T 0,8,1,0,3,0,5,0,7,0,9,0,2,0,4,0,6,0,8,0,10

%N A097807 * A002260.

%C Row sums = A002620: (1, 2, 4, 6, 9, 12, 16, 20, 25, 30, ...).

%C General case see A211161. Let B and C be sequences. By b(n) and c(n) denote elements B and C respectively. Table T(n,k) = b(n), if k is odd, c(k) if k is even read by antidiagonals. For this sequence b(n)=n, b(n)=A000027(n), c(n)=0, c(n)=A000004(n). - _Boris Putievskiy_, Feb 05 2013

%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations [of] Integer Sequences And Pairing Functions</a> arXiv:1212.2732 [math.CO], 2012.

%F A097807 * A002260 as infinite lower triangular matrices. k-th column = (k, 0, k, 0, ...).

%F From _Boris Putievskiy_, Feb 05 2013: (Start)

%F T(n,k) = (1-(-1)^k)*n/2;

%F a(n) = (1-(-1)^A004736(n))*A002260(n)/2;

%F a(n) = (1-(-1)^j)*i/2, where i = n-t*(t+1)/2, j = (t*t+3*t+4)/2-n, t = floor((-1+sqrt(8*n-7))/2). (End)

%e From _Boris Putievskiy_, Feb 05 2013: (Start)

%e The start of the sequence as a table:

%e 1, 0, 1, 0, 1, 0, 1, ...

%e 2, 0, 2, 0, 2, 0, 2, ...

%e 3, 0, 3, 0, 3, 0, 3, ...

%e 4, 0, 4, 0, 4, 0, 4, ...

%e 5, 0, 5, 0, 5, 0, 5, ...

%e 6, 0, 6, 0, 6, 0, 6, ...

%e 7, 0, 7, 0, 7, 0, 7, ...

%e ... (End)

%e First few rows of the triangle:

%e 1;

%e 0, 2;

%e 1, 0, 3;

%e 0, 2, 0, 4;

%e 1, 0, 3, 0, 5;

%e 0, 2, 0, 4, 0, 6;

%e 1, 0, 3, 0, 5, 0, 7;

%e ...

%Y Cf. A000004, A000027, A002260, A002620, A004736, A097807, A211161.

%K nonn,tabl

%O 1,3

%A _Gary W. Adamson_, Feb 17 2007