A172252 a(n) = 4*2^n - 9.

-1, 7, 23, 55, 119, 247, 503, 1015, 2039, 4087, 8183, 16375, 32759, 65527, 131063, 262135, 524279, 1048567, 2097143, 4194295, 8388599, 16777207, 33554423, 67108855, 134217719, 268435447, 536870903, 1073741815, 2147483639, 4294967287, 8589934583, 17179869175, 34359738359

Offset: 1

Author

Artur Jasinski, Jan 29 2010

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A000225, A159741, A185346, A206853.

Programs

Mathematica

Table[4 2^n - 9, {n, 1, 100}]
LinearRecurrence[{3,-2},{-1,7},30] (* Harvey P. Dale, May 27 2021 *)

PARI

my(x='x+O('x^34)); Vec(x*(10*x-1)/((x-1)*(2*x-1))) \\ Elmo R. Oliveira, Jun 15 2025

Formula

a(n) = 2*a(n-1) + 9, a(1)= -1. - Vincenzo Librandi, Mar 20 2011

For n >= 3, a(n) = 8<+>(n+2), where operation <+> is defined in A206853. - Vladimir Shevelev, Feb 17 2012

From Elmo R. Oliveira, Jun 15 2025: (Start)

G.f.: x*(10*x-1)/((x-1)*(2*x-1)).

E.g.f.: 5 + exp(x)*(4*exp(x) - 9).

a(n) = A185346(n+2) = 4*A000225(n) - 5.

a(n) = A159741(n-1) - 1 for n > 1. (End)

Extensions

More terms from Elmo R. Oliveira, Jun 15 2025