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 A211161 Table T(n,k) = n, if k is odd, k/2 if k is even; n, k > 0, read by antidiagonals. 2
 1, 1, 2, 1, 1, 3, 2, 2, 1, 4, 1, 2, 3, 1, 5, 3, 2, 2, 4, 1, 6, 1, 3, 3, 2, 5, 1, 7, 4, 2, 3, 4, 2, 6, 1, 8, 1, 4, 3, 3, 5, 2, 7, 1, 9, 5, 2, 4, 4, 3, 6, 2, 8, 1, 10, 1, 5, 3, 4, 5, 3, 7, 2, 9, 1, 11, 6, 2, 5, 4, 4, 6, 3, 8, 2, 10, 1, 12, 1, 6, 3, 5, 5, 4, 7, 3 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS In general, 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. For this sequence b(n)=n, c(k)=k. Row T(n,k) is b(n),c(1),b(n),c(2),b(n),c(3),...Numbers c(1),c(2),c(3),... sandwiched between b(n)'s. For this sequence numbers 1,2,3,... (A000027) sandwiched between n's. LINKS Boris Putievskiy, Rows n = 1..140 of triangle, flattened Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012. FORMULA For the general case As table T(n,k) = (1+(-1)^k)*c(k/2)/2 - (-1+(-1)^k)*b(n)/2. As linear sequence a(n) = (1+(-1)^j)*c(j/2)/2 - (-1+(-1)^j)*b(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). For b(n) = n and c(k) = k: As table T(n,k) = (1+(-1)^k)*k/4 - (-1+(-1)^k)*n/2. As linear sequence a(n) = (1+(-1)^A004736(n))*A004736(n)/4 - (-1+(-1)^A004736(n))*A002260(n)/2. a(n) = (1+(-1)^j)*j/4 - (-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). EXAMPLE The start of the sequence as table for general case: b(1)..c(1)..b(1)..c(2)..b(1)..c(3)..b(1)..c(4)... b(2)..c(1)..b(2)..c(2)..b(2)..c(3)..b(2)..c(4)... b(3)..c(1)..b(3)..c(2)..b(3)..c(3)..b(3)..c(4)... b(4)..c(1)..b(4)..c(2)..b(4)..c(3)..b(4)..c(4)... b(5)..c(1)..b(5)..c(2)..b(5)..c(3)..b(5)..c(4)... b(6)..c(1)..b(6)..c(2)..b(6)..c(3)..b(6)..c(4)... b(7)..c(1)..b(7)..c(2)..b(7)..c(3)..b(7)..c(4)... b(8)..c(1)..b(8)..c(2)..b(8)..c(3)..b(8)..c(4)... . . . The start of the sequence as triangle array read by rows for general case: b(1); c(1),b(2); b(1),c(1),b(3); c(2),b(2),c(1),b(4); b(1),c(2),b(3),c(1),b(5); c(3),b(2),c(2),b(4),c(1),b(6); b(1),c(3),b(3),c(2),b(5),c(1),b(7); c(4),b(2),c(3),b(4),c(2),b(6),c(1),b(8); . . . Row number r contains r numbers. If r is odd  b(1),c((r-1)/2),b(3),c((r-1)/2-1),b(5),c((r-1)/2-2),...c(1),b(r). If r is even c(r/2),b(2),c(r/2-1),b(4),c(r/2-2),b(6),...c(1),b(r). The start of the sequence as table for b(n)=n and c(k)=k: 1..1..1..2..1..3..1..4... 2..1..2..2..2..3..2..4... 3..1..3..2..3..3..3..4... 4..1..4..2..4..3..4..4... 5..1..5..2..5..3..5..4... 6..1..6..2..6..3..6..4... 7..1..7..2..7..3..7..4... 8..1..8..2..8..3..8..4... . . . The start of the sequence as triangle array read by rows for b(n)=n and c(k)=k: 1; 1,2; 1,1,3; 2,2,1,4; 1,2,3,1,5; 3,2,2,4,1,6; 1,3,3,2,5,1,7; 4,2,3,4,2,6,1,8; . . . Row number r contains r numbers. If r is odd  1,(r-1)/2,3,(r-1)/2-1,5,(r-1)/2-2,...1,r. If r id even r/2,2,r/2-1,4,r/2-1,6,...1,r. PROG (Python) def a(n):     t=int((math.sqrt(8*n-7) - 1)/ 2)     i=n-t*(t+1)//2     j=(t*t+3*t+4)//2-n     return (1+(-1)**j)*j//4 - (-1+(-1)**j)*i//2 CROSSREFS Cf. A000027, A002260, A004736, A210530. Sequence in context: A345116 A278042 A338714 * A208101 A131333 A120643 Adjacent sequences:  A211158 A211159 A211160 * A211162 A211163 A211164 KEYWORD nonn,tabl AUTHOR Boris Putievskiy, Jan 30 2013 STATUS approved

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Last modified August 1 22:36 EDT 2021. Contains 346408 sequences. (Running on oeis4.)