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A295508
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Triangle read by rows, related to binary partitions of n.
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2
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0, 1, 0, 2, 1, 0, 3, 2, 1, 4, 3, 2, 0, 5, 4, 3, 1, 6, 5, 4, 2, 7, 6, 5, 3, 8, 7, 6, 4, 0, 9, 8, 7, 5, 1, 10, 9, 8, 6, 2, 11, 10, 9, 7, 3, 12, 11, 10, 8, 4, 13, 12, 11, 9, 5, 14, 13, 12, 10, 6, 15, 14, 13, 11, 7, 16, 15, 14, 12, 8, 0, 17, 16, 15, 13, 9, 1
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OFFSET
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0,4
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LINKS
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FORMULA
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Let L(n) = (length of binary representation of n) - 0^n then
T(n, k) = n if k=0 else n - 2^(k-1) for n >= 0 and 0 <= k <= L(n).
Sum_{k=0..L(n)} T(n,k) = A123753(n-1) for n>=1.
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EXAMPLE
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0;
1, 0;
2, 1, 0;
3, 2, 1;
4, 3, 2, 0;
5, 4, 3, 1;
6, 5, 4, 2;
7, 6, 5, 3;
8, 7, 6, 4, 0;
9, 8, 7, 5, 1;
10, 9, 8, 6, 2;
11, 10, 9, 7, 3;
12, 11, 10, 8, 4;
13, 12, 11, 9, 5;
14, 13, 12, 10, 6;
15, 14, 13, 11, 7;
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MAPLE
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A295508_row := proc(n) local i, s, z; s := n; i := n-1; z := 1;
while 0 <= i do s := s, i; i := i-z; z := z+z od; s end:
# Alternatively after formula:
T := (n, k) -> `if`(k=0, n, n - 2^(k-1)):
L := n -> nops(convert(n, base, 2)) - 0^n:
T_row := n -> seq(T(n, k), k=0..L(n)):
seq(T_row(n), n=0..17);
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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