cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A017222 a(n) = (9*n + 5)^2.

This page as a plain text file.
%I A017222 #27 Dec 29 2022 06:34:15
%S A017222 25,196,529,1024,1681,2500,3481,4624,5929,7396,9025,10816,12769,14884,
%T A017222 17161,19600,22201,24964,27889,30976,34225,37636,41209,44944,48841,
%U A017222 52900,57121,61504,66049,70756
%N A017222 a(n) = (9*n + 5)^2.
%H A017222 Vincenzo Librandi, <a href="/A017222/b017222.txt">Table of n, a(n) for n = 0..10000</a>
%H A017222 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A017222 a(n) = A017221(n)^2.
%F A017222 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, May 22 2012
%F A017222 G.f.: (25 + 121*x + 16*x^2)/(1-x)^3. - _R. J. Mathar_, Mar 20 2018
%F A017222 From _G. C. Greubel_, Dec 29 2022: (Start)
%F A017222 a(2*n+1) = 4*A017246(n).
%F A017222 a(n) = a(n-1) + 9*(18*n + 1).
%F A017222 E.g.f.: (25 + 171*x + 81*x^2)*exp(x). (End)
%t A017222 (9Range[0,30]+5)^2 (* or *) LinearRecurrence[{3,-3,1},{25,196,529},30] (* _Harvey P. Dale_, May 22 2012 *)
%o A017222 (Magma) [(9*n+5)^2: n in [0..35]]; // _Vincenzo Librandi_, Jul 24 2011
%o A017222 (PARI) a(n)=(9*n+5)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o A017222 (SageMath) [(9*n+5)^2 for n in range(41)] # _G. C. Greubel_, Dec 29 2022
%Y A017222 Sequences of the form (m*n+5)^2: A010864 (m=0), A000290 (m=1), A016754 (m=2), A016790 (m=3), A016814 (m=4), A016850 (m=5), A016970 (m=6), A017042 (m=7), A017126 (m=8), this sequence (m=9), A017330 (m=10), A017450 (m=11), A017582 (m=12).
%Y A017222 Cf. A017221, A017246.
%K A017222 nonn,easy
%O A017222 0,1
%A A017222 _N. J. A. Sloane_