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

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