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.

A017642 a(n) = (12*n+10)^2.

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%I A017642 #17 Jul 08 2025 06:15:08
%S A017642 100,484,1156,2116,3364,4900,6724,8836,11236,13924,16900,20164,23716,
%T A017642 27556,31684,36100,40804,45796,51076,56644,62500,68644,75076,81796,
%U A017642 88804,96100,103684,111556,119716
%N A017642 a(n) = (12*n+10)^2.
%H A017642 Harvey P. Dale, <a href="/A017642/b017642.txt">Table of n, a(n) for n = 0..1000</a>
%H A017642 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A017642 From _Wesley Ivan Hurt_, Dec 22 2020: (Start)
%F A017642 G.f.: 4*(25 + 46*x + x^2)/(1 - x)^3.
%F A017642 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3.
%F A017642 a(n) = 144*n^2 + 240*n + 100.
%F A017642 a(n) = A017641(n)^2. (End)
%e A017642 a(5) = (12*5+10)^2 = 70^2 = 4900.
%t A017642 (12*Range[0,30]+10)^2 (* or *) LinearRecurrence[{3,-3,1},{100,484,1156},30] (* _Harvey P. Dale_, May 08 2017 *)
%t A017642 CoefficientList[Series[4*(25 + 46 x + x^2)/(1 - x)^3, {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Dec 22 2020 *)
%o A017642 (PARI) a(n)=(12*n+10)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o A017642 (Magma) [(12*n+10)^2 : n in [0..40]]; // _Wesley Ivan Hurt_, Dec 22 2020
%Y A017642 Cf. A016969, A016970, A017641, A017643.
%K A017642 nonn,easy
%O A017642 0,1
%A A017642 _N. J. A. Sloane_