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A172043 a(n) = 5*n^2 - n + 1. 4

%I #26 Sep 08 2022 08:45:50

%S 1,5,19,43,77,121,175,239,313,397,491,595,709,833,967,1111,1265,1429,

%T 1603,1787,1981,2185,2399,2623,2857,3101,3355,3619,3893,4177,4471,

%U 4775,5089,5413,5747,6091,6445,6809,7183,7567,7961,8365,8779,9203,9637,10081

%N a(n) = 5*n^2 - n + 1.

%H Vincenzo Librandi, <a href="/A172043/b172043.txt">Table of n, a(n) for n = 0..1000</a>

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

%F G.f.: (1+2*x+7*x^2)/(1-x)^3. - _Vincenzo Librandi_, Jul 06 2012

%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Vincenzo Librandi_, Jul 06 2012

%F a(n) = 2*A005476(n)+1. - _Bruno Berselli_, Jul 06 2012

%t CoefficientList[Series[(7*x^2+2*x+1)/(1-x)^3,{x,0,40}],x] (* _Vincenzo Librandi_, Jul 06 2012 *)

%t Table[5n^2-n+1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,5,19},50] (* _Harvey P. Dale_, Aug 06 2022 *)

%o (Magma) [ 5*n^2-n+1: n in [0..50] ];

%o (PARI) a(n)=5*n^2-n+1 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A005476.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Jan 29 2010

%E Replaced definition with formula. - _N. J. A. Sloane_, Mar 03 2010

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)