A271828 a(n) = 4*n^3 - 18*n^2 + 27*n - 12.

1, 2, 15, 64, 173, 366, 667, 1100, 1689, 2458, 3431, 4632, 6085, 7814, 9843, 12196, 14897, 17970, 21439, 25328, 29661, 34462, 39755, 45564, 51913, 58826, 66327, 74440, 83189, 92598, 102691, 113492, 125025, 137314, 150383, 164256, 178957, 194510, 210939, 228268, 246521, 265722

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 15 2016

Keywords

• nonn
• easy

Comments

This sequence lists all positive integers n such that 2*n - 3 is a cube. Only for first term 2*n - 3 generates a negative cube that is -1. - Altug Alkan, Apr 15 2016

Links

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

Crossrefs

Cf. positive integers n such that 2*n + k is a cube: this sequence (k=-3), A050492 (k=-1), A268201 (k=1).

Programs

Magma

[((2*n-1)^3+3)/2: n in [0..40]];

Mathematica

Table[((2 n - 1)^3 + 3)/2, {n, 0, 41}] (* or *)
Rest@ CoefficientList[Series[x (1 - 2 x + 13 x^2 + 12 x^3)/(1 - x)^4, {x, 0, 42}], x] (* Michael De Vlieger, Apr 16 2016 *)
LinearRecurrence[{4,-6,4,-1},{1,2,15,64},70] (* Harvey P. Dale, Jun 06 2022 *)

PARI

lista(nn) = for(n=0, nn, print1(((2*n-1)^3+3)/2, ", ")); \\ Altug Alkan, Apr 15 2016

Formula

a(n+1) = A050492(n)+1.

G.f.: x*(1 - 2*x + 13*x^2 + 12*x^3)/(1 - x)^4. - Ilya Gutkovskiy, Apr 15 2016