|
| |
|
|
A060734
|
|
Natural numbers written as a square array ending in last row from left to right and rightmost column from bottom to top are read by antidiagonals downwards.
|
|
6
| |
|
|
1, 4, 2, 9, 3, 5, 16, 8, 6, 10, 25, 15, 7, 11, 17, 36, 24, 14, 12, 18, 26, 49, 35, 23, 13, 19, 27, 37, 64, 48, 34, 22, 20, 28, 38, 50, 81, 63, 47, 33, 21, 29, 39, 51, 65, 100, 80, 62, 46, 32, 30, 40, 52, 66, 82, 121, 99, 79, 61, 45, 31, 41, 53, 67, 83, 101
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| A simple permutation of natural numbers.
Parity of the sequence is given by A057211 (n-th run has length n). [From Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Dec 26 2008]
The square with corners T(1,1)=1 and T(n,n)=n^2-n+1 is occupied by the numbers 1,2,...,n^2. - Clark Kimberling, Feb 01 2011
|
|
|
LINKS
| Index entries for sequences that are permutations of the natural numbers
Alois P. Heinz, Table of n, a(n) for n = 1..10011
|
|
|
FORMULA
| T(n,k) = (n-1)^2+k, T(k, n)=n^2+1-k, 1 <= k <= n.
T(1,k) = k^2 (A000290). - Clark Kimberling, Feb 01 2011
T(n,n) = n^2-n+1 (A002061) - Clark Kimberling, Feb 01 2011
T(n,1) = (n-1)^2+1 (A002522). - Clark Kimberling, Feb 01 2011
|
|
|
EXAMPLE
| Northwest corner:
.1 4 9 16 .. => a(1) = 1
.2 3 8 15 .. => a(2) = 4, a(3) = 2
.5 6 7 14 .. => a(4) = 9, a(5) = 3, a(6) = 5
10 11 12 13 .. => a(7) = 16, a(8) = 8, a(9) = 6, a(10)=10
|
|
|
MAPLE
| T:= (n, k)-> `if` (n<=k, k^2-n+1, (n-1)^2+k):
seq (seq (T(n, d-n), n=1..d-1), d=2..15);
|
|
|
MATHEMATICA
| f[n_, k_]:=k^2-n+1/; k>=n;
f[n_, k_]:=(n-1)^2+k/; k<n;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]]
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten (* Clark Kimberling, Feb 01 2011 *)
|
|
|
CROSSREFS
| Cf. A060736. Inverse: A064790.
Cf. A185725, A185726, A185728. - Clark Kimberling, Feb 01 2011
Sequence in context: A201574 A077809 A201281 * A075594 A076022 A064421
Adjacent sequences: A060731 A060732 A060733 * A060735 A060736 A060737
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Frank Ellermann (Frank.Ellermann(AT)t-online.de), Apr 23 2001
|
|
|
EXTENSIONS
| Corrected by Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Dec 26 2008
|
| |
|
|
