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%I #15 Jul 10 2023 21:50:34
%S 1,4,13,32,66,121,204,323,487,706,991,1354,1808,2367,3046,3861,4829,
%T 5968,7297,8836,10606,12629,14928,17527,20451,23726,27379,31438,35932,
%U 40891,46346,52329,58873,66012,73781,82216,91354,101233,111892,123371,135711
%N Number of length n strings on the alphabet {0,1,2,3} with digit sum at most 4.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = (((n + 10)*n + 35)*n + 26)*n/24 + 1.
%F G.f.: -(x^4 - 3*x^3 + 3*x^2 - x + 1)/(x - 1)^5.
%F a(n) = 1 + A005718(n-1) for n>=1.
%e For n=2, the 13 strings are all possible 2-character strings of '0', '1', '2' and '3' except the four strings '33', '32', '23'.
%t f[n_, r_, l_] := If[r < 0, 0, If[r==0, 1, If[l < 0, 0, If[l == 0, 1, Sum[f[n, r-j, l-1], {j, 0, n}]]]]]; Table[f[3, 4,x], {x, 0, 40}]
%Y Cf. A227259 (the same for {0,1,2} with digit sum <= 4).
%Y Cf. A105163 (the same for {0,1,2} with digit sum <= 3, shifted by 2).
%Y Cf. A005718.
%K nonn,easy
%O 0,2
%A _Daniel T. Martin_, May 23 2023
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