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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
OFFSET
1,2
COMMENTS
Intersection of this sequence and A001082 is {0, 21, 1365, 87381,...} all of the form (2^(6*m)-1)/3.
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 A372292
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Aug 12 2006
EXTENSIONS
0 added and b-file updated by Bruno Berselli, May 23 2017
STATUS
approved