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a(1)=1; thereafter, a(n+1) = 20*n^3 + 10*n.
6

%I #22 Sep 08 2022 08:45:16

%S 1,30,180,570,1320,2550,4380,6930,10320,14670,20100,26730,34680,44070,

%T 55020,67650,82080,98430,116820,137370,160200,185430,213180,243570,

%U 276720,312750,351780,393930,439320,488070,540300,596130,655680,719070,786420,857850

%N a(1)=1; thereafter, a(n+1) = 20*n^3 + 10*n.

%C Shells (nexus numbers) of shells of the fifth powers (A000584).

%H G. C. Greubel, <a href="/A101098/b101098.txt">Table of n, a(n) for n = 1..5000</a>

%H O. Bagdasar, <a href="http://www.np.ac.rs/downloads/publications/VOL6_Br_2/vol6br2-3.pdf">On some functions involving the lcm and gcd of integer tuples</a>, Scientific Publications of the State University of Novi Pazar, Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91--100.

%H C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, Explorations and Formulas of the Euler/Pascal Cube</a>.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F From _R. J. Mathar_, Sep 02 2008: (Start)

%F a(n) = A068236(n-2), n > 1.

%F G.f.: x + 30*x^2*(1+x)^2/(1-x)^4. (End)

%p a:=`if`(n=1,1,20*n^3+10*n): 1,seq(a(n),n=1..35); # _Muniru A Asiru_, Dec 02 2018

%t Table[If[n == 1, 1, 10*(n - 1)*(2*(n - 1)^2 + 1)], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 19 2011 *)(* modified by _G. C. Greubel_, Dec 01 2018 *)

%o (PARI) my(x='x+O('x^50)); Vec(x + 30*x^2*(1+x)^2/(1-x)^4) \\ _G. C. Greubel_, Dec 01 2018

%o (Magma) [n le 1 select 1 else 10*(n - 1)*(2*(n - 1)^2 + 1): n in [1..50]]; // _G. C. Greubel_, Dec 01 2018

%o (Sage) s=(x + 30*x^2*(1+x)^2/(1-x)^4).series(x, 50); s.coefficients(x, sparse=False) # _G. C. Greubel_, Dec 01 2018

%o (GAP) Concatenation([1],List([1..35],n->20*n^3+10*n)); # _Muniru A Asiru_, Dec 02 2018

%K easy,nonn

%O 1,2

%A Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004

%E Edited by _Ralf Stephan_, Dec 16 2004