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A288429
a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4), where a(0) = 2, a(1) = 4, a(2) = 5, a(3) = 6.
3
2, 4, 5, 6, 9, 13, 18, 26, 38, 55, 80, 117, 171, 250, 366, 536, 785, 1150, 1685, 2469, 3618, 5302, 7770, 11387, 16688, 24457, 35843, 52530, 76986, 112828, 165357, 242342, 355169, 520525, 762866, 1118034, 1638558, 2401423, 3519456, 5158013, 7559435, 11078890
OFFSET
0,1
COMMENTS
Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->0101, 1->100, starting with 00; see A288426.
FORMULA
a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4), where a(0) = 2, a(1) = 4, a(2) = 5. a(3) = 6.
G.f.: (2 - x^2 - 2*x^3)/(1 - 2*x + x^2 - x^3 + x^4).
a(n) = a(n-1) + a(n-3) - 1, for n > 2. - Greg Dresden, Feb 09 2020
MATHEMATICA
LinearRecurrence[{2, -1, 1, -1}, {2, 4, 5, 6}, 40]
CROSSREFS
Cf. A288426.
Sequence in context: A073894 A341496 A056635 * A163116 A003306 A250305
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 11 2017
STATUS
approved