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A176067
Binary analog of A098755 and A098756: Binary representation of least available nonnegative integer with bit values alternating for entire sequence.
0
1, 0, 10, 1010, 101010, 10101010, 1010101010, 101010101010, 10101010101010, 1010101010101010, 101010101010101010, 10101010101010101010, 1010101010101010101010, 101010101010101010101010, 10101010101010101010101010, 1010101010101010101010101010
OFFSET
-1,3
COMMENTS
Begin at a(-1) = 1 for A098756 analog; begin at a(0) = 0 for A098755 analog. A020988 gives the corresponding decimal representations for n >= 0; see relevant comments there and in A163662: This sequence is A163662 with 1, 0 prefixed.
FORMULA
a(n) = A007088(A020988(n)) for n >= 0; a(-1) = 1.
From Chai Wah Wu, Feb 11 2018: (Start)
a(n) = 101*a(n-1) - 100*a(n-2) for n > 1.
G.f.: (110*x^2 - 101*x + 1)/(x*(x - 1)*(100*x - 1)). (End)
MATHEMATICA
Join[{1, 0}, RecurrenceTable[{a[1]==10, a[2]==1010, a[n]==101 a[n-1] - 100 a[n-2]}, a, {n, 15}]] (* Vincenzo Librandi, Feb 11 2018 *)
PROG
(Magma) I:=[1, 0, 10]; [n le 3 select I[n] else 101*Self(n-1)-100*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 11 2018
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Rick L. Shepherd, Apr 07 2010
STATUS
approved