

A121628


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


3



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
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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)/(1x)^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: A275916 A129135 A158091 * A219154 A054257 A297316
Adjacent sequences: A121625 A121626 A121627 * A121629 A121630 A121631


KEYWORD

nonn,easy


AUTHOR

Zak Seidov, Aug 12 2006


EXTENSIONS

0 added and bfile updated by Bruno Berselli, May 23 2017


STATUS

approved



