A143096 a(n) = 2*a(n-1)-1, with a(1)=1, a(2)=4, a(3)=5.

1, 4, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649, 4294967297, 8589934593

Offset: 1

Author

Gary W. Adamson and Roger L. Bagula, Jul 23 2008

Keywords

• nonn
• easy

Examples

			a(4) = 9 = 2*a(3) - 1 = 2*5 - 1.
a(4) = 9 = (1, 3, 3, 1) dot (1, 3, -2, 5) = (1 + 9 - 6 + 5).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A065190.

Essentially the same as A083318, A048578 and A000051.

Programs

Mathematica

Join[{1,4},NestList[2#-1&,5,40]] (* or *) Join[{1,4},LinearRecurrence[ {3,-2},{5,9},40]] (* Harvey P. Dale, Feb 18 2014 *)

Formula

Binomial transform of 0, 1, 2, -4, 9, -13, 20, -26, 35, ... (offset 0).

O.g.f.: x*(1+x-5*x^2+2*x^3)/((1-x)*(1-2*x)). a(n) = 1+2^(n-1), n>2. - R. J. Mathar, Jul 31 2008

a(n) = A048578(n-2), n>=3. - R. J. Mathar, Aug 10 2008