# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a210535 Showing 1-1 of 1 %I A210535 #22 Nov 29 2023 06:57:42 %S A210535 1,2,1,2,3,1,2,4,3,1,2,4,5,3,1,2,4,6,5,3,1,2,4,6,7,5,3,1,2,4,6,8,7,5, %T A210535 3,1,2,4,6,8,9,7,5,3,1,2,4,6,8,10,9,7,5,3,1,2,4,6,8,10,11,9,7,5,3,1,2, %U A210535 4,6,8,10,12,11,9,7,5,3,1,2,4,6,8,10,12 %N A210535 Second inverse function (numbers of columns) for pairing function A209293. %H A210535 Boris Putievskiy, Rows n = 1..140 of triangle, flattened %H A210535 Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012. %H A210535 Eric Weisstein's World of Mathematics, Pairing functions %F A210535 a(n) = 2*A200260(n)-A101688(n)*(4*A002260(n)-2*A003056(n)-3). %F A210535 a(n) = 2*i-v*(4*i-2*t-3), where t = floor((-1+sqrt(8*n-7))/2), i = n-t*(t+1)/2, v = floor((2*n+1-t*(t+1))/(t+3)). %e A210535 The start of the sequence as triangle array read by rows: %e A210535 1; %e A210535 2,1; %e A210535 2,3,1; %e A210535 2,4,3,1; %e A210535 2,4,5,3,1; %e A210535 2,4,6,5,3,1; %e A210535 2,4,6,7,5,3,1; %e A210535 2,4,6,8,7,5,3,1; %e A210535 . . . %e A210535 Row number r contains permutation numbers from 1 to r: 2,4,6,...2*floor(r/2),2*floor(r/2)-1,2*floor(r/2)-3,...3,1. %o A210535 (Python) %o A210535 t=int((math.sqrt(8*n-7)-1)/2) %o A210535 i=n-t*(t+1)/2 %o A210535 v=int((2*n+1-t*(t+1))/(t+3)) %o A210535 result=2*i-v*(4*i-2*t-3) %Y A210535 Cf. A209293, A200260, A101688, A003056, A220073. %K A210535 nonn %O A210535 1,2 %A A210535 _Boris Putievskiy_, Jan 28 2013 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE