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A284979 Array a(m, n) giving the number of reversible strings with n beads of m colors, read by antidiagonals. 2
1, 1, 2, 1, 3, 3, 1, 6, 6, 4, 1, 10, 18, 10, 5, 1, 20, 45, 40, 15, 6, 1, 36, 135, 136, 75, 21, 7, 1, 72, 378, 544, 325, 126, 28, 8, 1, 136, 1134, 2080, 1625, 666, 196, 36, 9, 1, 272, 3321, 8320, 7875, 3996, 1225, 288, 45, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A277504 for additional information.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275

FORMULA

a(m, n) = (m^n + m^((n + mod(n,2))/2))/2.

EXAMPLE

Array begins:

1  1   1    1     1      1       1        1         1 ...

2  3   6   10    20     36      72      136       272 ...

3  6  18   45   135    378    1134     3321      9963 ...

4 10  40  136   544   2080    8320    32896    131584 ...

5 15  75  325  1625   7875   39375   195625    978125 ...

6 21 126  666  3996  23436  140616   840456   5042736 ...

7 28 196 1225  8575  58996  412972  2883601  20185207 ...

8 36 288 2080 16640 131328 1050624  8390656  67125248 ...

9 45 405 3321 29889 266085 2394765 21526641 193739769 ...

...

MATHEMATICA

a[n_, k_] :=  (k^n + k^((n + Mod[n, 2])/2))/2; Table[a[k - n + 1, n], {k, 1, 10}, {n, 1, k}] // Flatten (* Jean-Fran├žois Alcover, Oct 01 2017 *)

CROSSREFS

Transpose of A277504.

Sequence in context: A066704 A262917 A165007 * A127123 A271238 A186740

Adjacent sequences:  A284976 A284977 A284978 * A284980 A284981 A284982

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Apr 06 2017

STATUS

approved

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Last modified August 4 07:32 EDT 2020. Contains 336201 sequences. (Running on oeis4.)