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

1,2

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

Links

Reinhard Zumkeller, >Rows n = 1..125 of triangle, flattened

Index entries for sequences that are permutations of the natural numbers

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A024431, A115408, A247414.

Sequence in context: A254373 A343564 A004446 * A010775 A010485 A194362

Adjacent sequences: A115406 A115407 A115408 * A115410 A115411 A115412

Keyword

nonn,tabl,look

Author

Reinhard Zumkeller, Jan 22 2006

Status

approved