A101098 a(1)=1; thereafter, a(n+1) = 20*n^3 + 10*n.

1, 30, 180, 570, 1320, 2550, 4380, 6930, 10320, 14670, 20100, 26730, 34680, 44070, 55020, 67650, 82080, 98430, 116820, 137370, 160200, 185430, 213180, 243570, 276720, 312750, 351780, 393930, 439320, 488070, 540300, 596130, 655680, 719070, 786420, 857850

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• O. Bagdasar, On some functions involving the lcm and gcd of integer tuples, Scientific Publications of the State University of Novi Pazar, Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91--100.
• C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

GAP

Concatenation([1],List([1..35],n->20*n^3+10*n)); # Muniru A Asiru, Dec 02 2018

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

Maple

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

Mathematica

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 *)

PARI

my(x='x+O('x^50)); Vec(x + 30*x^2*(1+x)^2/(1-x)^4) \\ G. C. Greubel, Dec 01 2018

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

Formula

From R. J. Mathar, Sep 02 2008: (Start)

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

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

Extensions

Edited by Ralf Stephan, Dec 16 2004