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0, 0, 0, 1, 1, 1, 3, 3, 3, 7, 8, 9, 12, 13, 14, 19, 20, 21, 30, 33, 36, 42, 45, 48, 57, 60, 63, 79, 86, 93, 103, 111, 119, 132, 141, 150, 168, 180, 192, 209, 222, 235, 257, 271, 285, 316, 335, 354, 380, 400, 420, 453, 474, 495, 543, 573, 603, 639, 672, 705, 747
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,7
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LINKS
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FORMULA
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Let b(0) = 1 and b(n) = b(n-1) + b(floor(n/3)) and let c(n) = Product_{i=0..k}(n_i+1) where n = Sum_{i=0..k}n_i*3^i is the ternary representation of n. Then a(n) = (1/3)*(b(n) - c(n)).
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MATHEMATICA
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b[n_] := b[n] = If[n <= 2, n+1, b[n-1] + b[Floor[n/3]]];
c = Nest[Join[#, 2#, 3#]&, {1}, 4];
a[n_] := (b[n] - c[[n+1]])/3;
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PROG
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(Sage)
def b(n):
A=[1]
for i in [1..n]:
A.append(A[i-1] + A[floor(i/3)])
return A[n]
[(b(n)-prod(x+1 for x in n.digits(3)))/3 for n in [0..60]]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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