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1, 2, 2, 4, 6, 7, 10, 12, 18, 25, 31, 41, 56, 73, 96, 128, 171, 226, 302, 399, 533, 704, 937, 1236, 1645, 2170, 2884, 3806, 5059, 6680, 8875, 11725, 15575, 20584, 27332, 36132, 47963, 63420, 84160, 111306, 147673, 195345, 259118, 342831, 454680
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OFFSET
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1,2
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COMMENTS
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The average multiplicative growth from the n-th term to the (n+1)st term is the largest root of x^3 - x - 1, which is approximately 1.324718. - Nathaniel Johnston, Jan 13 2011
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,2,1,0,-2,-2,0,2,2,0,-1,-1).
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FORMULA
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G.f.: x*(1 + 2*x - x^3 - x^5 + x^8 + 5*x^9 + x^10 - 4*x^11 - 4*x^12 - 2*x^13 + x^14 + 4*x^15 + 3*x^16 - x^17) / ((1 - x)*(1 + x)*(1 + x^2)*(1 - x^2 - x^3)*(1 - x^2 + x^5)).
a(n) = 2*a(n-2) + a(n-3) - 2*a(n-5) - 2*a(n-6) + 2*a(n-8) + 2*a(n-9) - a(n-11) - a(n-12) for n>18.
(End)
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MATHEMATICA
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p={-1, 3, 4, 1, -2, -4, -4, 1, 5, 1, 0, 0, -1, 0, -1, 0, 2, 1};
q={1, 1, 0, -2, -2, 0, 2, 2, 0, -1, -2, 0, 1};
gf=Fold[x #1+#2&, 0, p]/Fold[x #1+#2&, 0, q];
LinearRecurrence[{0, 2, 1, 0, -2, -2, 0, 2, 2, 0, -1, -1}, {1, 2, 2, 4, 6, 7, 10, 12, 18, 25, 31, 41, 56, 73, 96, 128, 171, 226}, 50] (* Harvey P. Dale, Mar 08 2022 *)
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PROG
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(PARI) Vec(x*(1 + 2*x - x^3 - x^5 + x^8 + 5*x^9 + x^10 - 4*x^11 - 4*x^12 - 2*x^13 + x^14 + 4*x^15 + 3*x^16 - x^17) / ((1 - x)*(1 + x)*(1 + x^2)*(1 - x^2 - x^3)*(1 - x^2 + x^5)) + O(x^50)) \\ Colin Barker, Jul 01 2020
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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