A131833 a(n) = 2^(n+1) - 1 + 3*n.

1, 6, 13, 24, 43, 78, 145, 276, 535, 1050, 2077, 4128, 8227, 16422, 32809, 65580, 131119, 262194, 524341, 1048632, 2097211, 4194366, 8388673, 16777284, 33554503, 67108938, 134217805, 268435536, 536870995, 1073741910, 2147483737, 4294967388, 8589934687, 17179869282

Offset

0,2

Comments

Binomial transform of (1, 5, 2, 2, 2, ...).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

G.f.: (-1 - 2*x + 6*x^2)/((2*x - 1)*(x - 1)^2). - R. J. Mathar, Apr 04 2012

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - Vincenzo Librandi, Jul 05 2012

E.g.f.: exp(x)*(2*exp(x) - 1 + 3*x). - Stefano Spezia, Mar 29 2023

Example

a(3) = 24 = sum of row 3 terms of triangle A131832: (7 + 5 + 5 + 7).
a(3) = 24 = (1, 3, 3, 1) dot (1, 5, 2, 2) = (1 + 15 + 6 + 2).

Mathematica

CoefficientList[Series[(-1-2*x+6*x^2)/((2*x-1)*(x-1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 05 2012 *)
Table[2^(n+1)-1+3n, {n, 0, 30}] (* or *) LinearRecurrence[{4, -5, 2}, {1, 6, 13}, 40] (* Harvey P. Dale, Nov 06 2012 *)

Prog

(Magma) I:=[1, 6, 13]; [n le 3 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 05 2012

Crossrefs

Row sums of triangle A131832.

Sequence in context: A235450 A032528 A058535 * A101736 A162432 A117072

Adjacent sequences: A131830 A131831 A131832 * A131834 A131835 A131836

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 20 2007

Extensions

New definition by R. J. Mathar, Apr 04 2012

Status

approved