cp's OEIS Frontend

A109857 Next 2*n - 1 odd numbers in decreasing order followed by next 2*n even numbers in decreasing order.

%I A109857 #14 Jul 29 2023 17:38:29
%S A109857 1,4,2,7,5,3,12,10,8,6,17,15,13,11,9,24,22,20,18,16,14,31,29,27,25,23,
%T A109857 21,19,40,38,36,34,32,30,28,26,49,47,45,43,41,39,37,35,33,60,58,56,54,
%U A109857 52,50,48,46,44,42,71,69,67,65,63,61,59,57,55,53,51,84,82,80,78,76,74
%N A109857 Next 2*n - 1 odd numbers in decreasing order followed by next 2*n even numbers in decreasing order.
%C A109857 This sequence is a permutation of the positive integers. - _Werner Schulte_, Jul 29 2023
%F A109857 From _Werner Schulte_, Jul 29 2023: (Start)
%F A109857 T(n, k) = n*(n+1)/2 + floor(n/2) - 2*(k-1)  for 1 <= k <= n.
%F A109857 T(n, n) = (n^2-3*n+4)/2 + floor(n/2)  for n > 0.
%F A109857 T(2*n-1, n) = n^2 + (n-1)^2 = A001844(n-1)  for n > 0. (End)
%e A109857  1;
%e A109857  4,  2;
%e A109857  7,  5,  3;
%e A109857 12, 10,  8,  6;
%e A109857 17, 15, 13, 11,  9;
%e A109857 24, 22, 20, 18, 16, 14;
%e A109857 31, 29, 27, 25, 23, 21, 19;
%e A109857 40, 38, 36, 34, 32, 30, 28, 26;
%o A109857 (PARI) T(n,k)=n*(n+1)/2+floor(n/2)-2*(k-1) \\ _Werner Schulte_, Jul 29 2023
%Y A109857 Cf. A074147 (row reversed), A074149 (row sums), A074148 (column 1), A001844, A061925 (main diagonal).
%K A109857 easy,nonn,tabl
%O A109857 1,2
%A A109857 _Amarnath Murthy_, Jul 08 2005
%E A109857 More terms from _Joshua Zucker_, May 05 2006