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A168237
a(n) = (6*n + 3*(-1)^n - 3)/4.
4
0, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 66, 66, 69, 69, 72, 72, 75, 75, 78, 78, 81, 81, 84, 84, 87, 87, 90, 90, 93, 93, 96, 96, 99, 99, 102, 102, 105, 105
OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000 [a(0)=0 added by Georg Fischer, Feb 02 2021]
FORMULA
From R. J. Mathar, Jan 05 2011: (Start)
a(n) = 3*A110654(n-1) for n >= 1.
G.f.: 3*x^2 / ( (1+x)*(x-1)^2 ). (End)
a(n) = a(n-1) + a(n-2) - a(n-3). - Vincenzo Librandi, Sep 16 2013
E.g.f.: 3*(exp(x)*x - sinh(x))/2. - G. C. Greubel, Jul 16 2016
a(n) = 3*floor(n/2). - Daniel Checa, Mar 10 2024
MATHEMATICA
CoefficientList[Series[3*x^2/((1 + x)*(x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 16 2013 *)
Table[(6*n + 3*(-1)^n - 3)/4, {n, 0, 50}] (* or *)
LinearRecurrence[{1, 1, -1}, {0, 0, 3, 3}, 50] (* G. C. Greubel, Jul 16 2016 *)
With[{c=Range[0, 108, 3]}, Riffle[c, c]] (* Harvey P. Dale, Feb 03 2021 *)
PROG
(Magma) [3*n/2-3/4+3*(-1)^n/4: n in [0..70]]; // Vincenzo Librandi, Sep 16 2013
CROSSREFS
Sequence in context: A227128 A061795 A110261 * A290966 A049318 A325861
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 21 2009
EXTENSIONS
New definition by R. J. Mathar, Jan 05 2011
a(0)=0 added by N. J. A. Sloane, Feb 02 2021 at the suggestion of Allan C. Wechsler
STATUS
approved