A063497 Number of atoms in first n shells of type I hyperfullerene.

0, 60, 300, 840, 1800, 3300, 5460, 8400, 12240, 17100, 23100, 30360, 39000, 49140, 60900, 74400, 89760, 107100, 126540, 148200, 172200, 198660, 227700, 259440, 294000, 331500, 372060, 415800, 462840, 513300, 567300, 624960, 686400, 751740, 821100, 894600

Offset: 0

Author

N. J. A. Sloane, Aug 01 2001

Keywords

• nonn
• easy

Comments

The third derivative of the sum of 5th powers: A000539. - Gregory R. Bryant, Jun 14 2013

References

• T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (14).

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000539.

Programs

Magma

[20*n^3 + 30*n^2 + 10*n : n in [0..50]]; // Wesley Ivan Hurt, May 03 2021

Mathematica

Table[20n^3 + 30n^2 + 10n, {n, 0, 50}] (* David Nacin, Mar 01 2012 *)

PARI

a(n) = { 20*n^3 + 30*n^2 + 10*n } \\ Harry J. Smith, Aug 23 2009

Formula

a(n) = 20*n^3 + 30*n^2 + 10*n.

G.f.: 60*x * (1 + x)/(1 - x)^4. - Colin Barker, Mar 01 2012