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A195824
a(n) = 24*n^2.
6
0, 24, 96, 216, 384, 600, 864, 1176, 1536, 1944, 2400, 2904, 3456, 4056, 4704, 5400, 6144, 6936, 7776, 8664, 9600, 10584, 11616, 12696, 13824, 15000, 16224, 17496, 18816, 20184, 21600, 23064, 24576, 26136, 27744, 29400, 31104, 32856, 34656, 36504
OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 24,..., in the square spiral whose vertices are the generalized tetradecagonal numbers A195818.
Surface area of a cube with side 2n. - Wesley Ivan Hurt, Aug 05 2014
FORMULA
a(n) = 24*A000290(n) = 12*A001105(n) = 8*A033428(n) = 6*A016742(n) = 4*A033581(n) = 3*A139098(n) = 2*A135453(n).
G.f.: 24*x*(1+x)/(1-x)^3. - Wesley Ivan Hurt, Aug 05 2014
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Wesley Ivan Hurt, Aug 05 2014
MAPLE
A195824:=n->24*n^2: seq(A195824(n), n=0..50); # Wesley Ivan Hurt, Aug 05 2014
MATHEMATICA
24 Range[0, 30]^2 (* or *) Table[24 n^2, {n, 0, 30}] (* or *) CoefficientList[Series[24 x (1 + x)/(1 - x)^3, {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 05 2014 *)
LinearRecurrence[{3, -3, 1}, {0, 24, 96}, 40] (* Harvey P. Dale, Nov 11 2017 *)
PROG
(Magma) [24*n^2 : n in [0..50]]; // Wesley Ivan Hurt, Aug 05 2014
(PARI) a(n) = 24*n^2; \\ Michel Marcus, Aug 05 2014
(Magma) I:=[0, 24, 96]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Aug 06 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 28 2011
STATUS
approved