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

1,3

Links

Table of n, a(n) for n=1..56.

Index entries for linear recurrences with constant coefficients, signature (0, 4, 0, -6, 0, 4, 0, -1).

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.

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 *)

Prog

(Magma) &cat[ [ n, n^3 ]: n in [1..40] ]; // Vincenzo Librandi, Apr 21 2011

Crossrefs

Cf. A000463, A109588, A109594-5, A109614-6, A110001, A110003-5, A110008-9, A110485, A110622, A110650-3.

Sequence in context: A193976 A264244 A292930 * A282637 A256411 A218609

Adjacent sequences: A126948 A126949 A126950 * A126952 A126953 A126954

Keyword

nonn

Author

Zak Seidov, Mar 18 2007

Status

approved