A121628 Nonnegative k such that 3*k + 1 is a perfect cube.

0, 21, 114, 333, 732, 1365, 2286, 3549, 5208, 7317, 9930, 13101, 16884, 21333, 26502, 32445, 39216, 46869, 55458, 65037, 75660, 87381, 100254, 114333, 129672, 146325, 164346, 183789, 204708, 227157, 251190, 276861, 304224, 333333, 364242, 397005

Offset

1,2

Comments

Intersection of this sequence and A001082 is {0, 21, 1365, 87381,...} all of the form (2^(6*m)-1)/3.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 3*(n - 1)*(3*n^2 - 3*n + 1) with n>0. Corresponding cubes are 3*a(n) + 1 = (3*n - 2)^3.

G.f.: 3*x^2*(7 + 10*x + x^2)/(1-x)^4. - Colin Barker, Apr 11 2012

Mathematica

CoefficientList[Series[3 (7 + 10 x + x^2)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 11 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 21, 114, 333}, 40] (* Harvey P. Dale, Mar 08 2018 *)

Prog

(Magma) [3*n*(1+3*n+3*n^2): n in [1..40]]; // Vincenzo Librandi, Apr 11 2012

Crossrefs

Cf. A001082: 3*m + 1 is a perfect square.

Cf. A287335 (see Crossrefs).

Sequence in context: A355510 A129135 A158091 * A306532 A219154 A054257

Adjacent sequences: A121625 A121626 A121627 * A121629 A121630 A121631

Keyword

nonn,easy

Author

Zak Seidov, Aug 12 2006

Extensions

0 added and b-file updated by Bruno Berselli, May 23 2017

Status

approved