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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 (list; graph; refs; listen; history; text; internal format)
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: A275916 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

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)