A195323 - OEIS

%I #30 Dec 01 2024 20:16:15

%S 0,22,88,198,352,550,792,1078,1408,1782,2200,2662,3168,3718,4312,4950,

%T 5632,6358,7128,7942,8800,9702,10648,11638,12672,13750,14872,16038,

%U 17248,18502,19800,21142,22528,23958,25432,26950,28512,30118,31768,33462,35200,36982,38808

%N a(n) = 22*n^2.

%C Sequence found by reading the line from 0, in the direction 0, 22, ..., in the square spiral whose vertices are the generalized tridecagonal numbers A195313. Semi-axis opposite to A195318 in the same spiral.

%C Surface area of a rectangular prism with dimensions n, 2n and 3n. - _Wesley Ivan Hurt_, Apr 10 2015

%H Vincenzo Librandi, <a href="/A195323/b195323.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 22*A000290(n) = 11*A001105(n) = 2*A033584(n).

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Sep 19 2011

%F G.f.: 22*x*(1+x)/(1-x)^3. - _Wesley Ivan Hurt_, Apr 10 2015

%F From _Elmo R. Oliveira_, Dec 01 2024: (Start)

%F E.g.f.: 22*x*(1 + x)*exp(x).

%F a(n) = n*A008604(n) = A195149(2*n). (End)

%p A195323:=n->22*n^2: seq(A195323(n), n=0..80); # _Wesley Ivan Hurt_, Apr 10 2015

%t 22Range[0,50]^2 (* or *) LinearRecurrence[{3,-3,1},{0,22,88},50] (* _Harvey P. Dale_, Sep 19 2011 *)

%o (Magma) [22*n^2 : n in [0..40]]; // _Vincenzo Librandi_, Sep 20 2011

%o (PARI) vector(50,n,22*(n-1)^2) \\ _Derek Orr_, Apr 10 2015

%Y Bisection of A195149.

%Y Cf. A016802, A033581, A033583, A135453, A139098, A144555, A195321, A195322.

%Y Cf. A000290, A001105, A008604, A033584, A195313, A195318.

%K nonn,easy

%O 0,2

%A _Omar E. Pol_, Sep 16 2011