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 A288687 Number of n-digit biquanimous strings using digits {0,1,2,3}. 2

%I

%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

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Last modified January 21 19:39 EST 2019. Contains 319350 sequences. (Running on oeis4.)