A292523 Decimal encoding T(n,k) of the k-th non-averaging permutation of [n]; triangle T(n,k), n >= 0, k = 1..A003407(n), read by rows.

0, 1, 12, 21, 132, 213, 231, 312, 1324, 1342, 2143, 2413, 2431, 3124, 3142, 3412, 4213, 4231, 15324, 15342, 21453, 24153, 24315, 24351, 24513, 31254, 31524, 31542, 35124, 35142, 35412, 42153, 42315, 42351, 42513, 45213, 51324, 51342, 153264, 153426, 153462

Offset

0,3

Comments

A non-averaging permutation avoids any 3-term arithmetic progression.

The encoding of the empty permutation () is 0. For positive n each element in the permutation is encoded using 1+floor(log_10(n)) = A055642(n) digits with leading 0's if necessary. Then all elements are concatenated.

All terms are in increasing order.

Links

Alois P. Heinz, Rows n = 0..14, flattened

Eric Weisstein's World of Mathematics, Nonaveraging Sequence

Wikipedia, Arithmetic progression

Index entries related to non-averaging sequences

Example

Triangle T(n,k) begins:
:            0;
:            1;
:           12, 21;
:          132, 213, 231, 312;
:         1324, 1342, 2143, 2413,  2431,    3124,  3142, 3412, 4213, 4231;
:        15324, 15342, 21453, 24153,    ...,    42513, 45213, 51324, 51342;
:       153264, 153426, 153462, 153624, ..., 624153, 624315, 624351, 624513;
:      1532764, 1537264, 1537426,       ...,       7351462, 7351624, 7356124;
:     15327648, 15327684, 15372648,     ...,     84627351, 84672315, 84672351;
:    195327648, 195327684, 195372648,   ...,   915738462, 915783426, 915783462;
:   1090503020710060408,                ...,               10020608090401050703;
:  109050302110710060408,               ...,              1103070910010502060804;
: 10905031107021006041208,              ...,             120408100206110307090105;

Maple

T:= proc(n) option remember; local b, l, c; b, l, c:=
      proc(s, p) local ok, i, j, k;
        if nops(s) = 0 then l:= [l[], parse(p)]
      else for j in s do ok, i, k:= true, j-1, j+1;
             while ok and i>0 and k<=n do ok, i, k:=
               not i in s xor k in s, i-1, k+1 od;
             `if`(ok, b(s minus {j}, cat(p, 0$(c-length(j)), j)), 0)
           od
        fi
      end, [], length(n); b({$1..n}, "0"): sort(l)[]
    end:
seq(T(n), n=0..6);

Crossrefs

Cf. A003407, A030299, A055642, A088370.

Sequence in context: A268532 A260275 A001292 * A162391 A114015 A065439

Adjacent sequences: A292520 A292521 A292522 * A292524 A292525 A292526

Keyword

nonn,tabf,base

Author

Alois P. Heinz, Dec 08 2017

Status

approved