%I #14 Dec 16 2017 11:49:52
%S 1,1,4,19,92,421,1830,7687,31624,128521,518666,2084875,8361996,
%T 33497101,134094862,536608783,2146926608,8588754961,34357248018,
%U 137433710611,549744803860,2199000186901,8796044787734,35184271425559,140737278640152,562949517213721
%N Number of n-digit biquanimous strings using digits {0,1,2,3}.
%C A biquanimous string is a string whose digits can be split into two groups with equal sums.
%H Alois P. Heinz, <a href="/A288687/b288687.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10,-37,64,-52,16).
%F G.f.: (1 - 9*x + 31*x^2 - 48*x^3 + 38*x^4 - 16*x^5) / ((1 - x)^2*(1 - 2*x)^2*(1 - 4*x)).
%F a(n) = 1 + A064671(n) for n > 0.
%F From _Colin Barker_, Dec 16 2017: (Start)
%F a(n) = (2^(2*n-1) + n - 2^(n-1)*(1+n)).
%F a(n) = 10*a(n-1) - 37*a(n-2) + 64*a(n-3) - 52*a(n-4) + 16*a(n-5) for n>5.
%F (End)
%t LinearRecurrence[{10,-37,64,-52,16},{1,1,4,19,92,421},30] (* _Harvey P. Dale_, Jul 29 2017 *)
%o (PARI) Vec((1 - 9*x + 31*x^2 - 48*x^3 + 38*x^4 - 16*x^5) / ((1 - x)^2*(1 - 2*x)^2*(1 - 4*x)) + O(x^30)) \\ _Colin Barker_, Dec 16 2017
%Y Column k=3 of A288638.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Jun 13 2017