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A109614
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n^3 followed by n followed by n^2.
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2
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1, 1, 1, 8, 2, 4, 27, 3, 9, 64, 4, 16, 125, 5, 25, 216, 6, 36, 343, 7, 49, 512, 8, 64, 729, 9, 81, 1000, 10, 100, 1331, 11, 121, 1728, 12, 144, 2197, 13, 169, 2744, 14, 196, 3375, 15, 225, 4096, 16, 256, 4913, 17, 289, 5832, 18, 324, 6859, 19, 361, 8000, 20, 400
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listen;
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OFFSET
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1,4
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,-6,0,0,4,0,0,-1).
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FORMULA
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a(n) = 4*a(n-3) - 6*a(n-6) + 4*a(n-9) - a(n-12).
G.f.: -(-1-x-x^2-4*x^3+2*x^4-x^6-x^7+x^8)/((x-1)^4*(1+x+x^2)^4). (End)
a(n) = floor((n+2)/3)^((-3*(n mod 3)^2 + 5*(n mod 3) + 4)/2). - Luce ETIENNE, Mar 01 2018
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MATHEMATICA
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Table[{n^3, n, n^2}, {n, 20}]//Flatten (* or *) LinearRecurrence[{0, 0, 4, 0, 0, -6, 0, 0, 4, 0, 0, -1}, {1, 1, 1, 8, 2, 4, 27, 3, 9, 64, 4, 16}, 60] (* Harvey P. Dale, Feb 25 2016 *)
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PROG
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(Haskell)
import Data.List (transpose)
a109614 n = a109614_list !! (n-1)
a109614_list = concat $ transpose
[tail a000578_list, a000027_list, tail a000290_list]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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