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A363256
Number of length n strings on the alphabet {0,1,2,3} with digit sum at most 4.
0
1, 4, 13, 32, 66, 121, 204, 323, 487, 706, 991, 1354, 1808, 2367, 3046, 3861, 4829, 5968, 7297, 8836, 10606, 12629, 14928, 17527, 20451, 23726, 27379, 31438, 35932, 40891, 46346, 52329, 58873, 66012, 73781, 82216, 91354, 101233, 111892, 123371, 135711
OFFSET
0,2
FORMULA
a(n) = (((n + 10)*n + 35)*n + 26)*n/24 + 1.
G.f.: -(x^4 - 3*x^3 + 3*x^2 - x + 1)/(x - 1)^5.
a(n) = 1 + A005718(n-1) for n>=1.
EXAMPLE
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'.
MATHEMATICA
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}]
CROSSREFS
Cf. A227259 (the same for {0,1,2} with digit sum <= 4).
Cf. A105163 (the same for {0,1,2} with digit sum <= 3, shifted by 2).
Cf. A005718.
Sequence in context: A212747 A011936 A037235 * A051912 A060099 A208638
KEYWORD
nonn,easy
AUTHOR
Daniel T. Martin, May 23 2023
STATUS
approved