cp's OEIS Frontend

A128179 A097807 * A002260.

%I A128179 #17 Feb 15 2022 09:53:55
%S A128179 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 A128179 0,8,1,0,3,0,5,0,7,0,9,0,2,0,4,0,6,0,8,0,10
%N A128179 A097807 * A002260.
%C A128179 Row sums = A002620: (1, 2, 4, 6, 9, 12, 16, 20, 25, 30, ...).
%C A128179 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 A128179 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 A128179 A097807 * A002260 as infinite lower triangular matrices. k-th column = (k, 0, k, 0, ...).
%F A128179 From _Boris Putievskiy_, Feb 05 2013: (Start)
%F A128179 T(n,k) = (1-(-1)^k)*n/2;
%F A128179 a(n) = (1-(-1)^A004736(n))*A002260(n)/2;
%F A128179 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 A128179 From _Boris Putievskiy_, Feb 05 2013: (Start)
%e A128179 The start of the sequence as a table:
%e A128179   1, 0, 1, 0, 1, 0, 1, ...
%e A128179   2, 0, 2, 0, 2, 0, 2, ...
%e A128179   3, 0, 3, 0, 3, 0, 3, ...
%e A128179   4, 0, 4, 0, 4, 0, 4, ...
%e A128179   5, 0, 5, 0, 5, 0, 5, ...
%e A128179   6, 0, 6, 0, 6, 0, 6, ...
%e A128179   7, 0, 7, 0, 7, 0, 7, ...
%e A128179   ... (End)
%e A128179 First few rows of the triangle:
%e A128179   1;
%e A128179   0, 2;
%e A128179   1, 0, 3;
%e A128179   0, 2, 0, 4;
%e A128179   1, 0, 3, 0, 5;
%e A128179   0, 2, 0, 4, 0, 6;
%e A128179   1, 0, 3, 0, 5, 0, 7;
%e A128179   ...
%Y A128179 Cf. A000004, A000027, A002260, A002620, A004736, A097807, A211161.
%K A128179 nonn,tabl
%O A128179 1,3
%A A128179 _Gary W. Adamson_, Feb 17 2007