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A289060 a(n) = 3*a(n-1) - 3*a(n-2) + *a(n-3) for n >= 8, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 17, a(5) = 25, a(6) = 36, a(7) = 51. 2
2, 4, 7, 11, 17, 25, 36, 51, 70, 93, 120, 151, 186, 225, 268, 315, 366, 421, 480, 543, 610, 681, 756, 835, 918, 1005, 1096, 1191, 1290, 1393, 1500, 1611, 1726, 1845, 1968, 2095, 2226, 2361, 2500, 2643, 2790, 2941, 3096, 3255, 3418, 3585, 3756, 3931, 4110 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iterate of the mapping 00->0010, 01->010, 10->011, starting with 00; see A289057.
LINKS
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 8, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 17, a(5) = 25, a(6) = 36, a(7) = 51.
G.f.: (-2 + 2*x - x^2 - x^4 - x^6 - x^7)/(-1 + x)^3.
a(n) = 30 - 11*n + 2*n^2 for n>4. - Colin Barker, Jul 02 2017
MATHEMATICA
Join[{2, 4, 7, 11, 17}, LinearRecurrence[{3, -3, 1}, {25, 36, 51}, 40]]
CROSSREFS
Cf. A288216.
Sequence in context: A073472 A096914 A004250 * A194805 A084842 A289177
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 27 2017
STATUS
approved

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Last modified March 29 09:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)