A134351 Binomial transform of [1, 5, -1, 5, -1, 5, ...]. Inverse binomial transform of A134350.

1, 6, 10, 18, 34, 66, 130, 258, 514, 1026, 2050, 4098, 8194, 16386, 32770, 65538, 131074, 262146, 524290, 1048578, 2097154, 4194306, 8388610, 16777218, 33554434, 67108866, 134217730, 268435458, 536870914, 1073741826, 2147483650, 4294967298, 8589934594

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 2 + 2^(n+1) for n >= 1; a(0)=1. - Emeric Deutsch, Oct 24 2007

O.g.f.: (-1-3*x+6*x^2)/((1-x)*(-1+2*x)). - R. J. Mathar, Apr 02 2008

From Elmo R. Oliveira, Jul 06 2026: (Start)

E.g.f.: 2*exp(x)*(1 + exp(x)) - 3.

a(n) = 2*A048578(n-1) for n > 0.

a(n) = 3*a(n-1) - 2*a(n-2) for n > 2. (End)

Example

a(3) = 18 = (1, 3, 3, 1) dot (1, 5, -1, 5) = (1 + 15 - 3 + 5).

Maple

1, seq(2^(n+1)+2, n=1..25); # Emeric Deutsch, Oct 24 2007

Prog

(PARI) a(n) = if(n==0, 1, 2 + 2^(n+1)) \\ Andrew Howroyd, Sep 14 2025

Crossrefs

Essentially the same as A133140, A089985, A052548.

Cf. A048578, A134350.

Sequence in context: A169873 A363788 A079471 * A307458 A338450 A287273

Adjacent sequences: A134348 A134349 A134350 * A134352 A134353 A134354

Keyword

nonn,easy,changed

Author

Gary W. Adamson, Oct 21 2007

Extensions

More terms from Emeric Deutsch, Oct 24 2007

More terms from R. J. Mathar, Apr 02 2008

Offset corrected and more terms from Andrew Howroyd, Sep 14 2025

Status

approved