A155640 a(n) = 7^n - 5^n + 1^n.

1, 3, 25, 219, 1777, 13683, 102025, 745419, 5374177, 38400483, 272709625, 1928498619, 13597146577, 95668307283, 672119557225, 4717043931819, 33080342678977, 231867574534083, 1624598900644825, 11379821699045019, 79696898865971377, 558069026925080883

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,-47,35).

Crossrefs

Cf. A155624, A155625, A155626, A155627, A155628, A155629, A155630, A155631, A155632, A155633, A155634, A155635, A155636, A155637, A155638, A155639.

Programs

Mathematica

Table[7^n - 5^n + 1, {n, 0, 25}] (* Paolo Xausa, Jul 26 2024 *)

PARI

a(n)=7^n-5^n+1 \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f.: 1/(1-7*x)-1/(1-5*x)+1/(1-x).

E.g.f.: e^(7*x)-e^(5*x)+e^x.

a(n) = 12*a(n-1)-35*a(n-2)+24 with a(0)=1, a(1)=3. - Vincenzo Librandi, Jul 21 2010