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a(n) = (5*n + 2)^2.
2

%I #33 May 07 2024 06:26:37

%S 4,49,144,289,484,729,1024,1369,1764,2209,2704,3249,3844,4489,5184,

%T 5929,6724,7569,8464,9409,10404,11449,12544,13689,14884,16129,17424,

%U 18769,20164,21609,23104,24649,26244

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

%H Vincenzo Librandi, <a href="/A016874/b016874.txt">Table of n, a(n) for n = 0..2000</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/PolygammaFunction.html">Polygamma Function</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Polygamma_function">Polygamma Function</a>.

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

%F a(n) = a(n-1) + 50*n - 5; a(0)=4. - _Vincenzo Librandi_, Jun 07 2011

%F Sum_{n>=0} 1/a(n) = polygamma(1, 2/5)/25 = 0.2910142636... - _Amiram Eldar_, Oct 02 2020

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Wesley Ivan Hurt_, Oct 02 2020

%F G.f.: -(4+x)*(1+9*x)/(-1+x)^3. - _Wesley Ivan Hurt_, Oct 02 2020

%e a(0) = (5*0 + 2)^2 = 4.

%t (5*Range[0,40]+2)^2 (* _Harvey P. Dale_, Feb 19 2011 *)

%o (Magma) [(5*n+2)^2: n in [0..40]]; // _Vincenzo Librandi_, Jun 07 2011

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

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_