A272342 a(n) = 27*8^n.

27, 216, 1728, 13824, 110592, 884736, 7077888, 56623104, 452984832, 3623878656, 28991029248, 231928233984, 1855425871872, 14843406974976, 118747255799808, 949978046398464, 7599824371187712, 60798594969501696

Offset: 0

Author

Andres Cicuttin, Apr 26 2016

Keywords

• nonn
• easy

Comments

a(n) are cubes that can be expressed as sum of exactly four distinct powers of two: a(n)=2^3n + 2^(3n+1) + 2^(3n+3) + 2^(3n+4). For example a(0) = 2^0 + 2^1 + 2^3 + 2^4 = 1 + 2 + 8 + 16 = 27. It is conjectured the a(n) are the only cubes that can be expressed as sum of exactly four distinct nonnegative powers of two (tested on cubes up to (10^7)^3).

Links

• Index entries for linear recurrences with constant coefficients, signature (8).

Crossrefs

Cf. A001018, A002063.

Programs

Mathematica

nmax=120; 27*8^Range[0, nmax]

PARI

a(n) = 27*8^n; \\ Michel Marcus, Apr 27 2016

Formula

a(n) = 27*8^n = 2^3n + 2^(3n+1) + 2^(3n+3) + 2^(3n+4).

a(n) = 8*a(n-1), n>0; a(0)=27.

G.f.: 27/(1-8*x).

E.g.f.: 27*exp(8*x).

a(n) = 27*A001018(n). - Michel Marcus, Apr 26 2016