cp's OEIS Frontend

A065025 Consider biquanimous numbers that exclude 0's; sequence gives number of n-digit non-biquanimous numbers - number of n-digit biquanimous numbers.

%I A065025 #27 Feb 20 2021 03:58:22
%S A065025 9,63,513,3423,18589,73035,225479,617215,1622001,4300263,12128763,
%T A065025 37076783,122411649,427600575,1550703157,5759666431,21738733961,
%U A065025 82999762711,319722139579,1240393764207,4840363237201,18979321319087,74713018378209,295061102101311
%N A065025 Consider biquanimous numbers that exclude 0's; sequence gives number of n-digit non-biquanimous numbers - number of n-digit biquanimous numbers.
%C A065025 A biquanimous number (A064544) is a number whose digits can be split into two groups with equal sums.
%D A065025 _William P. Thurston_, personal communication.
%D A065025 _William P. Thurston_, Biquanimous Generating Function, math-fun mailing list, November 2001.
%H A065025 Alois P. Heinz, <a href="/A065025/b065025.txt">Table of n, a(n) for n = 1..1660</a>
%H A065025 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (17, -114, 348, -228, -1524, 3888, -216, -11046, 11382, 12012, -26544, 84, 28812, -13152, -15816, 13407, 3201, -5834, 628, 984, -288).
%F A065025 From _Alois P. Heinz_, Jun 12 2017: (Start)
%F A065025 G.f.: -x*(988416*x^33 +272448*x^32 -6983328*x^31 -2873424*x^30 +20931912*x^29 +11886288*x^28 -33545700*x^27 -25677164*x^26 +28467368*x^25 +29854804*x^24 -7032026*x^23 -11748538*x^22 -12593064*x^21 -17118040*x^20 +24399398*x^19 +29412358*x^18 -32880510*x^17 -15770937*x^16 +33016792*x^15 -4824040*x^14 -21307320*x^13 +10258240*x^12 +7474762*x^11 -5162898*x^10 -999324*x^9 +1008806*x^8 +39654*x^7 -89810*x^6 +3200*x^5 +992*x^4 +1248*x^3 -468*x^2 +90*x -9) / ((4*x-1) *(3*x-1)^2 *(2*x-1)^3 *(x+1)^7 *(x-1)^8).
%F A065025 a(n) = 9^n - 2 * A288550(n). (End)
%Y A065025 Cf. A064544, A065023, A065024, A288550.
%K A065025 nonn,base,easy
%O A065025 1,1
%A A065025 _N. J. A. Sloane_, Nov 03 2001
%E A065025 New offset and 4 more terms from _Alois P. Heinz_, Jun 11 2017