A158056 - OEIS

%I #25 Sep 08 2022 08:45:42

%S 18,68,150,264,410,588,798,1040,1314,1620,1958,2328,2730,3164,3630,

%T 4128,4658,5220,5814,6440,7098,7788,8510,9264,10050,10868,11718,12600,

%U 13514,14460,15438,16448,17490,18564,19670,20808,21978,23180,24414,25680

%N a(n) = 16*n^2 + 2*n.

%C The identity (16*n + 1)^2 - (16*n^2 + 2*n)*4^2 = 1 can be written as A158057(n)^2 - a(n)*4^2 = 1. - _Vincenzo Librandi_, Feb 09 2012

%C Sequence found by reading the line from 18, in the direction 18, 68, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 02 2012

%H Vincenzo Librandi, <a href="/A158056/b158056.txt">Table of n, a(n) for n = 1..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) = 3*a(n-1) - 3*a(n-2) + a(n-3).

%F G.f.: 2*x*(-9 - 7*x)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{18,68,150},50]

%t Table[16n^2+2n,{n,40}]  (* _Harvey P. Dale_, Apr 13 2011 *)

%o (Magma) I:=[18, 68, 150]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];

%o (PARI) a(n) = 16*n^2 + 2*n.

%Y Cf. A158057.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 12 2009