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A116526
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a(0)=1, a(1)=1, a(n) = 9*a(n/2) for even n >= 2, and a(n) = 8*a((n-1)/2) + a((n+1)/2) for odd n >= 3.
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5
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0, 1, 9, 17, 81, 89, 153, 217, 729, 737, 801, 865, 1377, 1441, 1953, 2465, 6561, 6569, 6633, 6697, 7209, 7273, 7785, 8297, 12393, 12457, 12969, 13481, 17577, 18089, 22185, 26281, 59049, 59057, 59121, 59185, 59697, 59761, 60273, 60785, 64881, 64945, 65457, 65969
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OFFSET
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0,3
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COMMENTS
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The interest this one has is in the prime form of even odd 2^n+1, 2^n.
Let M =
1, 0, 0, 0, 0, ...
9, 0, 0, 0, 0, ...
8, 1, 0, 0, 0, ...
0, 9, 0, 0, 0, ...
0, 8, 1, 0, 0, ...
0, 0, 9, 0, 0, ...
0, 0, 8, 1, 0, ...
...
Then M^k converges to a single nonzero column giving the sequence.
The sequence divided by its aerated variant is (1, 9, 8, 0, 0, 0, ...). (End)
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LINKS
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FORMULA
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MAPLE
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a:=proc(n) if n=0 then 0 elif n=1 then 1 elif n mod 2 = 0 then 9*a(n/2) else 8*a((n-1)/2)+a((n+1)/2) fi end: seq(a(n), n=0..45);
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MATHEMATICA
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b[0] := 0; b[1] := 1; b[n_?EvenQ] := b[n] = 9*b[n/2]; b[n_?OddQ] := b[n] = 8*b[(n - 1)/2] + b[(n + 1)/2]; a = Table[b[n], {n, 1, 25}]
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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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