A257505 - OEIS

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A257505

Square array A(row,col): A(row,1) = A256450(row-1), and for col > 1, A(row,col) = A255411(A(row,col-1)); Dispersion of factorial base shift A255411.

15

1, 4, 2, 18, 12, 3, 96, 72, 16, 5, 600, 480, 90, 22, 6, 4320, 3600, 576, 114, 48, 7, 35280, 30240, 4200, 696, 360, 52, 8, 322560, 282240, 34560, 4920, 2880, 378, 60, 9, 3265920, 2903040, 317520, 39600, 25200, 2976, 432, 64, 10, 36288000, 32659200, 3225600, 357840, 241920, 25800, 3360, 450, 66, 11, 439084800, 399168000, 35925120, 3588480, 2540160, 246240, 28800, 3456, 456, 70, 13

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The array is read by downward antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

In Kimberling's terminology, this array is called the dispersion of sequence A255411 (when started from its first nonzero term, 4). The left column is the complement of that sequence, which is A256450.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1275; the first 50 antidiagonals of array

Clark Kimberling, Interspersions and Dispersions.

Clark Kimberling, Interspersions and Dispersions, Proceedings of the American Mathematical Society, 117 (1993) 313-321.

Index entries for sequences related to factorial base representation

Index entries for sequences that are permutations of the natural numbers

FORMULA

A(row,1) = A256450(row-1), and for col > 1, A(row,col) = A255411(A(row,col-1)).

EXAMPLE

The top left corner of the array:

1, 4, 18, 96, 600, 4320, 35280, 322560, 3265920

2, 12, 72, 480, 3600, 30240, 282240, 2903040, 32659200

3, 16, 90, 576, 4200, 34560, 317520, 3225600, 35925120

5, 22, 114, 696, 4920, 39600, 357840, 3588480, 39553920

6, 48, 360, 2880, 25200, 241920, 2540160, 29030400, 359251200

7, 52, 378, 2976, 25800, 246240, 2575440, 29352960, 362517120

8, 60, 432, 3360, 28800, 272160, 2822400, 31933440, 391910400

9, 64, 450, 3456, 29400, 276480, 2857680, 32256000, 395176320

10, 66, 456, 3480, 29520, 277200, 2862720, 32296320, 395539200

11, 70, 474, 3576, 30120, 281520, 2898000, 32618880, 398805120

13, 76, 498, 3696, 30840, 286560, 2938320, 32981760, 402433920

14, 84, 552, 4080, 33840, 312480, 3185280, 35562240, 431827200

15, 88, 570, 4176, 34440, 316800, 3220560, 35884800, 435093120

17, 94, 594, 4296, 35160, 321840, 3260880, 36247680, 438721920

19, 100, 618, 4416, 35880, 326880, 3301200, 36610560, 442350720

20, 108, 672, 4800, 38880, 352800, 3548160, 39191040, 471744000

21, 112, 690, 4896, 39480, 357120, 3583440, 39513600, 475009920

23, 118, 714, 5016, 40200, 362160, 3623760, 39876480, 478638720

...

PROG

(Scheme)

(define (A257505 n) (A257505bi (A002260 n) (A004736 n)))

(define (A257505bi row col) (if (= 1 col) (A256450 (- row 1)) (A255411 (A257505bi row (- col 1)))))

CROSSREFS

Transpose: A257503.

Inverse permutation: A257506.

Row index: A257681, Column index: A257679.

Columns 1-3: A256450, A257692, A257693.

Rows 1-3: A001563, A062119, A130744 (without their initial zero-terms).

Row 4: A213167 (without the initial one).

Row 5: A052571 (without initial zeros).

Cf. A007623, A256450, A255411.

Cf. also permutations A255565, A255566.

Thematically similar arrays: A035513, A054582, A246279.

Sequence in context: A302461 A303243 A074676 * A152883 A285793 A117692

Adjacent sequences: A257502 A257503 A257504 * A257506 A257507 A257508

KEYWORD

nonn,base,tabl

AUTHOR

Antti Karttunen, Apr 27 2015

EXTENSIONS

Formula changed because of the changed starting offset of A256450 - Antti Karttunen, May 30 2016

STATUS

approved