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A049943
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a(n) = a(1) + a(2) + ... + a(n-1) + a(m) for n >= 3, where m = 2*n - 2 - 2^(p+1) and p is the unique integer such that 2^p < n-1 <= 2^(p+1), starting with a(1) = a(2) = 1.
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4
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1, 1, 3, 6, 17, 29, 63, 149, 418, 688, 1381, 2785, 5690, 11919, 25935, 61004, 171093, 281183, 562371, 1124765, 2249650, 4499839, 9001775, 18012684, 36074453, 72369085, 145581752, 294538578, 602590001, 1259536403, 2741242299, 6447482423, 18082910866, 29718339310
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = a(2*n - 2 - 2^ceiling(log_2(n-1))) + Sum_{i = 1..n-1} a(i) for n >= 3.
a(n) = a(1 + A006257(n-2)) + Sum_{i = 1..n-1} a(i) for n >= 3.
(End)
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EXAMPLE
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a(3) = a(1 + A006257(3-2)) + a(1) + a(2) = a(2) + a(1) + a(2) = 3;
a(4) = a(1 + A006257(4-2)) + a(1) + a(2) + a(3) = a(2) + a(1) + a(2) + a(3) = 6;
a(5) = a(1 + A006257(5-2)) + a(1) + a(2) + a(3) + a(4) = a(4) + a(1) + a(2) + a(3) + a(4) = 17. (End)
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MAPLE
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s := proc(n) option remember; `if`(n < 1, 0, a(n) + s(n - 1)); end proc:
a := proc(n) option remember;
`if`(n < 3, 1, s(n - 1) + a(2*n - 3 - Bits:-Iff(n - 2, n - 2)));
end proc:
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MATHEMATICA
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A006257[n_] := Boole[BitXor[n, #] < n]& /@ Range[n] // Total;
a[n_] := a[n] = If[n < 3, 1, a[1 + A006257[n-2]] + Total@Array[a, n-1]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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