A284979 Array a(m, n) giving the number of reversible strings with n beads of m colors, read by antidiagonals.

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

Offset: 1

Author

Andrew Howroyd, Apr 06 2017

Keywords

• nonn
• tabl

Comments

See A277504 for additional information.

Examples

			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 ...
...
		

Links

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

Crossrefs

Transpose of A277504.

Programs

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-François Alcover, Oct 01 2017 *)

Formula

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