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Number of n-digit biquanimous strings using digits {0,1,...,7}.
2

%I #5 Jun 14 2017 10:18:07

%S 1,1,8,85,988,10696,104676,939863,7980376,65679175,532115106,

%T 4279710436,34311898336,274729437763,2198561705222,17590732383423,

%U 140732804110800,1125884352801489,9007145852828686,72057404552774828,576460059887430848,4611683426113781209

%N Number of n-digit biquanimous strings using digits {0,1,...,7}.

%C A biquanimous string is a string whose digits can be split into two groups with equal sums.

%H Alois P. Heinz, <a href="/A288691/b288691.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (40, -734, 8256, -64063, 365480, -1593840, 5449456, -14855999, 32647032, -58206694, 84416480, -99491505, 94840120, -72455660, 43708272, -20343280, 7044608, -1708352, 258816, -18432).

%F G.f.: (9216*x^24 -129408*x^23+881824*x^22 -3910528*x^21 +12761816*x^20 -31636760*x^19 +62309010*x^18 -101187417*x^17 +139600728*x^16 -166854657*x^15 +174047204*x^14 -158809357*x^13 +127270681*x^12 -89880736*x^11 +55637484*x^10 -29668152*x^9 +13297571*x^8 -4887342*x^7 +1441132*x^6 -333899*x^5 +59267*x^4 -7757*x^3 +702*x^2 -39*x +1) / ((8*x-1) *(4*x-1) *(3*x-1)^2 *(2*x-1)^6 *(x-1)^10).

%Y Column k=7 of A288638.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Jun 13 2017