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A288260
a(n) = 2*a(n-1) + 2*a(n-3) - 3*a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 16.
3
2, 4, 8, 16, 34, 72, 152, 324, 690, 1468, 3128, 6664, 14194, 30240, 64424, 137244, 292386, 622900, 1327016, 2827072, 6022786, 12830904, 27334904, 58234164, 124061778, 264300652, 563064920, 1199550904, 2555517778, 5444263440, 11598433928, 24709250700
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->0010, 1->100, starting with 00; see A288257. [Mapping corrected by Michel Dekking, Mar 05 2020.]
Second Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->0101, 1->`010, starting with 00; see A288466. - Michel Dekking, Mar 05 2020
FORMULA
a(n) = 2*a(n-1) + 2*a(n-3) - 3*a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 16.
G.f.: -2*(-1+2*x^3)/(x-1)/(3*x^3+x^2+x-1) .
MATHEMATICA
LinearRecurrence[{2, 0, 2, -3}, {2, 4, 8, 16}, 40]
CROSSREFS
Sequence in context: A088325 A215930 A367660 * A006210 A288176 A096812
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 09 2017
STATUS
approved