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.
%I A195322 #92 Dec 01 2024 10:04:52
%S A195322 0,20,80,180,320,500,720,980,1280,1620,2000,2420,2880,3380,3920,4500,
%T A195322 5120,5780,6480,7220,8000,8820,9680,10580,11520,12500,13520,14580,
%U A195322 15680,16820,18000,19220,20480,21780,23120,24500,25920,27380,28880,30420,32000,33620,35280
%N A195322 a(n) = 20*n^2.
%C A195322 Sequence found by reading the line from 0, in the direction 0, 20, ..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. Semiaxis opposite to A195317 in the same spiral.
%C A195322 a(n) is the sum of all the integers less than 10*n which are not multiple of 2 or 5. a(2) = (1 + 3 + 7 + 9) + (11 + 13 + 17 + 19) = 20 + 60 = 80 = 20 * 2^2. (Link Crux Mathematicorum). - _Bernard Schott_, May 15 2017
%C A195322 Number of terms less than 10^k (k=0, 1, 2, ...): 1, 1, 3, 8, 23, 71, 224, 708, 2237, 7072, 22361, 70711, ... - _Muniru A Asiru_, Feb 01 2018
%H A195322 Vincenzo Librandi, <a href="/A195322/b195322.txt">Table of n, a(n) for n = 0..10000</a>
%H A195322 Léo Sauvé, <a href="https://cms.math.ca/crux/backfile/Crux_v1n09_Nov.pdf">Problem 53</a>, Crux Mathematicorum, Vol. 1, Nov. 1975, page 88.
%H A195322 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195322 a(n) = 20*A000290(n) = 10*A001105(n) = 5*A016742(n) = 4*A033429(n) = 2*A033583(n).
%F A195322 a(0)=0, a(1)=20, a(2)=80; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Jan 18 2013
%F A195322 a(n) = A010014(n) - A005899(n) for n > 0. - _R. J. Cano_, Sep 29 2015
%F A195322 From _Elmo R. Oliveira_, Nov 30 2024: (Start)
%F A195322 G.f.: 20*x*(1 + x)/(1-x)^3.
%F A195322 E.g.f.: 20*x*(1 + x)*exp(x).
%F A195322 a(n) = n*A008602(n) = A195148(2*n). (End)
%e A195322 From _Muniru A Asiru_, Feb 01 2018: (Start)
%e A195322 n=0, a(0) = 20*0^2 = 0.
%e A195322 n=1, a(1) = 20*1^2 = 20.
%e A195322 n=1, a(2) = 20*2^2 = 80.
%e A195322 n=1, a(3) = 20*3^2 = 180.
%e A195322 n=1, a(4) = 20*4^2 = 320.
%e A195322 ...
%e A195322 (End)
%p A195322 a := n -> 20*n^2; seq(a(n), n=0..10^3); # _Muniru A Asiru_, Feb 01 2018
%t A195322 20 Range[0, 40]^2 (* or *) LinearRecurrence[{3, -3, 1}, {0, 20, 80}, 50] (* _Harvey P. Dale_, Jan 18 2013 *)
%o A195322 (Magma) [20*n^2: n in [0..40]]; // _Vincenzo Librandi_, Sep 20 2011
%o A195322 (PARI) a(n) = 20*n^2 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A195322 (GAP) List([0..10^3],n->20*n^2); # _Muniru A Asiru_, Feb 01 2018
%Y A195322 Bisection of A195148.
%Y A195322 Cf. A016802, A033581, A033583, A135453, A139098, A144555, A195321, A195323.
%Y A195322 Cf. A000290, A001105, A005899, A010014, A016742, A033429, A195162, A195317.
%Y A195322 Cf. A008602.
%K A195322 nonn,easy
%O A195322 0,2
%A A195322 _Omar E. Pol_, Sep 16 2011