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%I #16 Mar 24 2022 20:25:08
%S 35,750,6174,31025,114961,346193,896876,2072694,4379055,8606312,
%T 15936426,28073487,47400509,77164915,121695128,186650684,279308283,
%U 408886194,586909430,827618109,1148421417,1570399589,2118856324,2823924050,3721224455,4852586700
%N Number of 8-digit positive integers in base n where the sum of the first k digits equals the sum of the last k digits.
%C These integers are sometimes called balanced numbers.
%D Cambridge Colleges Sixth Term Examination Papers (STEP) 2007, Paper I, Section A (Pure Mathematics), Nr. 1.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F a(n) = n*(n-1)*(1208*n^5+151*n^4+291*n^3+116*n^2+88*n+60)/2520.
%F G.f.: x^2*(x^5+83*x^4+673*x^3+1154*x^2+470*x+35)/(x-1)^8. - _Alois P. Heinz_, Mar 24 2022
%t Table[n(n-1)(1208n^5+151n^4+291n^3+116n^2+88n+60)/2520,{n,2,40}] (* _Harvey P. Dale_, Mar 18 2022 *)
%Y Cf. A016061, A197083, A240927, A240929.
%K nonn,base
%O 2,1
%A _Martin Renner_, Aug 03 2014
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