A195824 a(n) = 24*n^2.

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, 38400, 40344

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 24*A000290(n) = 12*A001105(n) = 8*A033428(n) = 6*A016742(n) = 4*A033581(n) = 3*A139098(n) = 2*A135453(n).

From Wesley Ivan Hurt, Aug 05 2014: (Start)

G.f.: 24*x*(1+x)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

From Elmo R. Oliveira, Dec 01 2024: (Start)

E.g.f.: 24*x*(1 + x)*exp(x).

a(n) = n*A008606(n) = A195158(2*n). (End)

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

Bisection of A195158.

Cf. A000290, A001105, A008606, A016742, A033428, A033581, A135453, A139098, A195818.

Sequence in context: A370846 A335144 A209432 * A183009 A272871 A319577

Adjacent sequences: A195821 A195822 A195823 * A195825 A195826 A195827

Keyword

nonn,easy

Author

Omar E. Pol, Sep 28 2011

Status

approved