A155629 a(n) = 8^n - 4^n + 1.

1, 5, 49, 449, 3841, 31745, 258049, 2080769, 16711681, 133955585, 1072693249, 8585740289, 68702699521, 549688705025, 4397778075649, 35183298347009, 281470681743361, 2251782633816065, 18014329790005249, 144114913197948929, 1152920405095219201, 9223367638808264705

Offset: 0

Author

Mohammad K. Azarian, Jan 30 2009

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (13,-44,32).

Crossrefs

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625, A155626, A155627, A155628.

Programs

Mathematica

Table[8^n - 4^n + 1, {n, 0, 25}] (* Paolo Xausa, Jul 30 2024 *)

PARI

a(n)=8^n-4^n+1 \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f.: 1/(1-8*x)-1/(1-4*x)+1/(1-x).

E.g.f.: exp(8*x)-exp(4*x)+exp(x).

a(n) = 12*a(n-1)-32*a(n-2)+21 with a(0) = 1, a(1) = 5. - Vincenzo Librandi, Jul 21 2010