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COMMENTS
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a(n) and differences:
1, 1, 2, 2, 3, 5, 9, 15, 24, 38, ... a(n)
0, 1, 0, 1, 2, 4, 6, 9, 14, 23, 38, ... b(n)
1, -1, 1, 1, 2, 2, 3, 5, 9, 15, 24, 38, ... a(n-2)
-2, 2, 0, 1, 0, 1, 2, 4, 6, 9, 14, 23, 38, ... b(n-2)
4, -2, 1,-1, 1, 1, 2, 2, 3, 5, 9, ... a(n-4)
-6, 3,-2, 2, 0, 1, 0, 1, 2, 4, 6, 9, ... b(n-4)
9, -5, 4,-2, 1,-1, 1, 1, 2, 2, 3, 5, 9, ... a(n-6)
-14, 9,-6, 3,-2, 2, 0, 1 0, 1, 2, ... b(n-6)
23,-15, 9,-5, 4,-2, 1, -1, 1, 1, 2, 2, ... a(n-8)
a(n)-b(n+1) = period 6: repeat 0, 1, 1, 0, -1, -1 = A128834(n).
Diagonals with the same number give 1, 2, 9, 38, ... = A001077(n).
Second column: the (n+2)-th term is identical to a(n+1) signed.
a(n+1) is identical to its twice shifted inverse binomial transform signed.
a(n+1)/a(n) tends to A001622 (the golden ratio) as n -> infinity.
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