A115409 Inverse integer permutation of A115408.

1, 5, 4, 7, 6, 2, 17, 16, 12, 10, 20, 19, 15, 13, 3, 43, 42, 38, 36, 26, 23, 51, 50, 46, 44, 34, 31, 8, 105, 104, 100, 98, 88, 85, 62, 54, 114, 113, 109, 107, 97, 94, 71, 63, 9

Offset: 1

Author

Reinhard Zumkeller, Jan 22 2006

Keywords

• nonn
• tabl
• look

Comments

Seen as a triangle read by rows T(n,k) = a(n*(n-1)/2+k) = A024431(n)-A024431(k-1), 1<=k<=n.

T(n,1) = A024431(n)-1; T(n,n) = A247414(n-1). - Reinhard Zumkeller, Sep 16 2014

Examples

			Triangle begins:
1;
5, 4;
7, 6, 2;
17, 16, 12, 10;
20, 19, 15, 13, 3;
...
		

Links

• Reinhard Zumkeller, >Rows n = 1..125 of triangle, flattened
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A024431, A115408, A247414.

Programs

Haskell

import Data.List (inits)
a115409 n k = a115409_tabl !! (n-1) !! (k-1)
a115409_row n = a115409_tabl !! (n-1)
a115409_tabl = map f $ drop 2 $ inits a024431_list where
   f xs = reverse $ map (z -) zs where (z:zs) = reverse xs
a115409_list = concat a115409_tabl
-- Reinhard Zumkeller, Sep 16 2014

Mathematica

nmax = 9;
differenceQ[seq_, x_] := Module[{r = False}, Do[If[x==seq[[k]] - seq[[j]], r = True; Break[]], {j, 1, Length[seq]}, {k, 1, Length[seq]}]; r];
seq[1] = {1, 2};
seq[i_] := seq[i] = Module[{j, k}, k = Max[seq[i-1]]; j = First[Select[ Range[k], !differenceQ[seq[i-1], #]&, 1]]; Union[seq[i-1], {2k+2, 2k+2+j}]];
A024431 = seq[nmax];
T[n_, k_] := A024431[[n+1]] -  A024431[[k]];
Table[T[n, k], {n, 1, nmax}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 20 2021 *)