A276955 Square array A(row,col): A(row,1) = A273670(row-1), and for col > 1, A(row,col) = A153880(A(row,col-1)); Dispersion of factorial base left shift A153880.

1, 2, 3, 6, 8, 4, 24, 30, 12, 5, 120, 144, 48, 14, 7, 720, 840, 240, 54, 26, 9, 5040, 5760, 1440, 264, 126, 32, 10, 40320, 45360, 10080, 1560, 744, 150, 36, 11, 362880, 403200, 80640, 10800, 5160, 864, 168, 38, 13, 3628800, 3991680, 725760, 85680, 41040, 5880, 960, 174, 50, 15, 39916800, 43545600, 7257600, 766080, 367920, 46080, 6480, 984, 246, 56, 16

Offset

1,2

Comments

The square array A(row,col) is read by descending antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

When viewed in factorial base (A007623) the terms on each row start all with the same prefix, but with an increasing number of zeros appended to the end. For example, for row 8 (A001344 from a(1)=11 onward), the terms written in factorial base look as: 121, 1210, 12100, 121000, ...

Links

Antti Karttunen, Table of n, a(n) for n = 1..1830; the first 60 antidiagonals of array

Index entries for sequences related to factorial base representation

Index entries for sequences that are permutations of the natural numbers

Formula

A(row,1) = A273670(row-1), and for col > 1, A(row,col) = A153880(A(row,col-1))

As a composition of other permutations:

a(n) = A275848(A257505(n)).

Example

The top left {1..9} x {1..18} corner of the array:
   1,  2,   6,   24,   120,    720,    5040,    40320,    362880
   3,  8,  30,  144,   840,   5760,   45360,   403200,   3991680
   4, 12,  48,  240,  1440,  10080,   80640,   725760,   7257600
   5, 14,  54,  264,  1560,  10800,   85680,   766080,   7620480
   7, 26, 126,  744,  5160,  41040,  367920,  3669120,  40279680
   9, 32, 150,  864,  5880,  46080,  408240,  4032000,  43908480
  10, 36, 168,  960,  6480,  50400,  443520,  4354560,  47174400
  11, 38, 174,  984,  6600,  51120,  448560,  4394880,  47537280
  13, 50, 246, 1464, 10200,  81360,  730800,  7297920,  80196480
  15, 56, 270, 1584, 10920,  86400,  771120,  7660800,  83825280
  16, 60, 288, 1680, 11520,  90720,  806400,  7983360,  87091200
  17, 62, 294, 1704, 11640,  91440,  811440,  8023680,  87454080
  18, 72, 360, 2160, 15120, 120960, 1088640, 10886400, 119750400
  19, 74, 366, 2184, 15240, 121680, 1093680, 10926720, 120113280
  20, 78, 384, 2280, 15840, 126000, 1128960, 11249280, 123379200
  21, 80, 390, 2304, 15960, 126720, 1134000, 11289600, 123742080
  22, 84, 408, 2400, 16560, 131040, 1169280, 11612160, 127008000
  23, 86, 414, 2424, 16680, 131760, 1174320, 11652480, 127370880

Prog

(Scheme)
(define (A276955 n) (A276955bi (A002260 n) (A004736 n)))
(define (A276955bi row col) (if (= 1 col) (A273670 (- row 1)) (A153880 (A276955bi row (- col 1)))))

Crossrefs

Inverse permutation: A276956.

Transpose: A276953.

Cf. A276949 (index of column where n appears), A276951 (index of row).

Cf. A153880.

Columns 1-3: A273670, A276932, A276933.

The following lists some of the rows that have their own entries. Pattern present in the factorial base expansion of the terms on that row is given in double quotes:

Row 1: A000142 (from a(1)=1, "1" onward),

Row 2: A001048 (from a(2)=3, "11" onward),

Row 3: A052849 (from a(2)=4, "20" onward).

Row 4: A052649 (from a(1)=5, "21" onward).

Row 5: A108217 (from a(3)=7, "101" onward).

Row 6: A054119 (from a(3)=9, "111" onward).

Row 7: A052572 (from a(2)=10, "120" onward).

Row 8: A001344 (from a(1)=11, "121" onward).

Row 13: A052560 (from a(3)=18, "300" onward).

Row 16: A225658 (from a(1)=21, "311" onward).

Row 20: A276940 (from a(3) = 27, "1011" onward).

Related or similar permutations: A257505, A275848, A273666.

Cf. also arrays A276617, A276588 & A276945.

Sequence in context: A349917 A191453 A191454 * A276945 A246266 A284385

Adjacent sequences: A276952 A276953 A276954 * A276956 A276957 A276958

Keyword

nonn,base,tabl

Author

Antti Karttunen, Sep 22 2016

Status

approved