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A288511
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a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 4*a(n-5) - 4*a(n-6) + 4*a(n-7) - 4*a(n-8) + 4*a(n-9) - 3*a(n-10) + 2*a(n-11) - 3*a(n-12) + 2*a(n-13) for n >= 16, with initial values as shown.
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3
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2, 4, 5, 7, 9, 12, 17, 23, 33, 48, 70, 103, 152, 228, 343, 515, 779, 1180, 1787, 2715, 4124, 6264, 9526, 14483, 22025, 33504, 50957, 77519, 117929, 179396, 272930, 415215, 631680, 961032, 1462067, 2224347, 3384083, 5148432, 7832727, 11916547, 18129540
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OFFSET
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0,1
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COMMENTS
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Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->0101, 10->001, starting with 00; see A288508.
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2, -1, 2, -4, 4, -4, 4, -4, 4, -3, 2, -3, 2).
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FORMULA
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G.f.: x*(2 - x^2 - 3*x^3 - x^5 - x^7 - x^9 - x^10 - 3*x^11 + x^12 + 2*x^13 + x^14- 2*x^15) / ((1 - x)^2*(1 - x^2 - 2*x^3)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Jun 12 2017
a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 4*a(n-5) - 4*a(n-6) + 4*a(n-7) - 4*a(n-8) + 4*a(n-9) - 3*a(n-10) + 2*a(n-11) - 3*a(n-12) + 2*a(n-13) for n >= 16, where a(0)=2, a(1)=4, a(2)=5, a(3)=7, a(4)=9, a(5)=12, a(6)=17, a(7)=23, a(8)=33, a(9)=48, a(10)=70, a(11)=103, a(12)=152, a(13)=228, a(14)=343, a(15)=515.
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MATHEMATICA
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Join[{2, 4, 5}, LinearRecurrence[{2, -1, 2, -4, 4, -4, 4, -4, 4, -3, 2, -3, 2}, {7, 9, 12, 17, 23, 33, 48, 70, 103, 152, 228, 343, 515}, 40]]
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PROG
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(PARI) Vec(x*(2 - x^2 - 3*x^3 - x^5 - x^7 - x^9 - x^10 - 3*x^11 + x^12 + 2*x^13 + x^14- 2*x^15) / ((1 - x)^2*(1 - x^2 - 2*x^3)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, Jun 12 2017
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CROSSREFS
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Cf. A288508.
Sequence in context: A275534 A069355 A212661 * A249058 A105771 A193494
Adjacent sequences: A288508 A288509 A288510 * A288512 A288513 A288514
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, Jun 12 2017
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STATUS
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approved
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