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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 26 08:16 EDT 2019. Contains 322472 sequences. (Running on oeis4.)