%I #10 Oct 01 2017 02:59:22
%S 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,
%T 7,1,72,378,544,325,126,28,8,1,136,1134,2080,1625,666,196,36,9,1,272,
%U 3321,8320,7875,3996,1225,288,45,10
%N Array a(m, n) giving the number of reversible strings with n beads of m colors, read by antidiagonals.
%C See A277504 for additional information.
%H Andrew Howroyd, <a href="/A284979/b284979.txt">Table of n, a(n) for n = 1..1275</a>
%F a(m, n) = (m^n + m^((n + mod(n,2))/2))/2.
%e Array begins:
%e 1 1 1 1 1 1 1 1 1 ...
%e 2 3 6 10 20 36 72 136 272 ...
%e 3 6 18 45 135 378 1134 3321 9963 ...
%e 4 10 40 136 544 2080 8320 32896 131584 ...
%e 5 15 75 325 1625 7875 39375 195625 978125 ...
%e 6 21 126 666 3996 23436 140616 840456 5042736 ...
%e 7 28 196 1225 8575 58996 412972 2883601 20185207 ...
%e 8 36 288 2080 16640 131328 1050624 8390656 67125248 ...
%e 9 45 405 3321 29889 266085 2394765 21526641 193739769 ...
%e ...
%t 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 *)
%Y Transpose of A277504.
%K nonn,tabl
%O 1,3
%A _Andrew Howroyd_, Apr 06 2017