A109594 n followed by n^3 followed by n^2.
1, 1, 1, 2, 8, 4, 3, 27, 9, 4, 64, 16, 5, 125, 25, 6, 216, 36, 7, 343, 49, 8, 512, 64, 9, 729, 81, 10, 1000, 100, 11, 1331, 121, 12, 1728, 144, 13, 2197, 169, 14, 2744, 196, 15, 3375, 225, 16, 4096, 256, 17, 4913, 289, 18, 5832, 324, 19, 6859, 361, 20, 8000, 400
Offset: 1
Links
- Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from Colin Barker)
- Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,-6,0,0,4,0,0,-1).
Programs
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Maple
map(t -> (t,t^3,t^2), [$1..100]); # Robert Israel, Dec 17 2017
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Mathematica
Flatten[Table[{n,n^3,n^2},{n,20}]] (* Harvey P. Dale, Jul 22 2012 *) -
PARI
Vec(x*(1+x+x^2-2*x^3+4*x^4+x^6+x^7-x^8)/((1-x)^4*(1+x+x^2)^4) + O(x^100)) \\ Colin Barker, Dec 02 2015
Formula
From Colin Barker, Dec 02 2015: (Start)
a(n) = 4*a(n-3) - 6*a(n-6) + 4*a(n-9) - a(n-12) for n > 12.
G.f.: x*(1+x+x^2-2*x^3+4*x^4+x^6+x^7-x^8) / ((1-x)^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, Dec 17 2017