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A333405 Number of integers in base n having exactly three distinct digits such that the number formed by the consecutive subsequence of the initial j digits is divisible by j for all j in {1,2,3}.

%I A333405 #30 Jul 03 2021 10:38:32
%S A333405 0,0,0,0,5,6,18,33,50,67,115,134,206,258,340,398,537,598,778,891,1086,
%T A333405 1209,1487,1614,1950,2148,2504,2716,3181,3398,3938,4245,4810,5135,
%U A333405 5835,6166,6958,7398,8220,8682,9665,10134,11226,11823,12950,13573,14887,15518
%N A333405 Number of integers in base n having exactly three distinct digits such that the number formed by the consecutive subsequence of the initial j digits is divisible by j for all j in {1,2,3}.
%H A333405 Alois P. Heinz, <a href="/A333405/b333405.txt">Table of n, a(n) for n = 0..10000</a>
%H A333405 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,0,2,-2,-2,2,0,0,-1,1,1,-1).
%F A333405 G.f.: (2*x^11+5*x^9+10*x^8+21*x^6+2*x^5+5*x^4+14*x^3+7*x^2+x+5)*x^4 / ((x^2+x+1)^2 *(x^2-x+1)^2 *(x+1)^3 *(x-1)^4).
%e A333405 a(4) = 5: 102, 120, 123, 201, 321 (written in base 4).
%e A333405 a(5) = 6: 132, 201, 204, 314, 402, 421 (written in base 5).
%e A333405 a(6) = 18: 103, 120, 123, 140, 143, 203, 240, 243, 320, 340, 403, 420, 423, 503, 520, 523, 540, 543 (written in base 6).
%Y A333405 Column k=3 of A334318.
%K A333405 nonn,easy
%O A333405 0,5
%A A333405 _Alois P. Heinz_, May 04 2020