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

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, 21, 19, 40, 38, 36, 34, 32, 30, 28, 26, 49, 47, 45, 43, 41, 39, 37, 35, 33, 60, 58, 56, 54, 52, 50, 48, 46, 44, 42, 71, 69, 67, 65, 63, 61, 59, 57, 55, 53, 51, 84, 82, 80, 78, 76, 74

Offset

1,2

Comments

This sequence is a permutation of the positive integers. - Werner Schulte, Jul 29 2023

Links

Table of n, a(n) for n=1..72.

Formula

From Werner Schulte, Jul 29 2023: (Start)

T(n, k) = n*(n+1)/2 + floor(n/2) - 2*(k-1) for 1 <= k <= n.

T(n, n) = (n^2-3*n+4)/2 + floor(n/2) for n > 0.

T(2*n-1, n) = n^2 + (n-1)^2 = A001844(n-1) for n > 0. (End)

Example

 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, 21, 19;
40, 38, 36, 34, 32, 30, 28, 26;

Prog

(PARI) T(n, k)=n*(n+1)/2+floor(n/2)-2*(k-1) \\ Werner Schulte, Jul 29 2023

Crossrefs

Cf. A074147 (row reversed), A074149 (row sums), A074148 (column 1), A001844, A061925 (main diagonal).

Sequence in context: A021963 A131914 A115302 * A194075 A271479 A259927

Adjacent sequences: A109854 A109855 A109856 * A109858 A109859 A109860

Keyword

easy,nonn,tabl

Author

Amarnath Murthy, Jul 08 2005

Extensions

More terms from Joshua Zucker, May 05 2006

Status

approved