A126951 List of pairs: k followed by k^3.
1, 1, 2, 8, 3, 27, 4, 64, 5, 125, 6, 216, 7, 343, 8, 512, 9, 729, 10, 1000, 11, 1331, 12, 1728, 13, 2197, 14, 2744, 15, 3375, 16, 4096, 17, 4913, 18, 5832, 19, 6859, 20, 8000, 21, 9261, 22, 10648, 23, 12167, 24, 13824, 25, 15625, 26, 17576, 27, 19683, 28, 21952
Offset: 1
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (0, 4, 0, -6, 0, 4, 0, -1).
Crossrefs
Programs
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Magma
&cat[ [ n, n^3 ]: n in [1..40] ]; // Vincenzo Librandi, Apr 21 2011
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Mathematica
Table[((((-1)^(n+1))+1)/4)(n+1)- ((((-1)^(n+1))-1)/16)n^3,{n,64}] Flatten[Table[{n,n^3},{n,30}]] (* or *) LinearRecurrence[{0,4,0,-6,0,4,0,-1},{1,1,2,8,3,27,4,64},60] (* Harvey P. Dale, Mar 11 2018 *)
Formula
a(n) = (n+1)/2 if n is odd, a(n) = (n/2)^3 otherwise;
a(n) = ((((-1)^(n+1))+1)/4)*(n+1) - ((((-1)^(n+1))-1)/16)*n^3;
g.f.: (x + x^2 - 2*x^3 + 4*x^4 + x^5 + x^6)/(1 - x^2)^4.