A048474 a(n) = 3*n*2^(n-1) + 1.

1, 4, 13, 37, 97, 241, 577, 1345, 3073, 6913, 15361, 33793, 73729, 159745, 344065, 737281, 1572865, 3342337, 7077889, 14942209, 31457281, 66060289, 138412033, 289406977, 603979777, 1258291201, 2617245697, 5435817985

Offset

0,2

Comments

Original name: a(n) = T(2, n), array T given by A048472.

Binomial transform of A008486. - Paul Barry, Jul 09 2003

Row sums of triangle A134232. - Gary W. Adamson, Oct 14 2007

Links

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

Index entries for linear recurrences with constant coefficients, signature (5, -8, 4).

Formula

From Harvey P. Dale, Jan 29 2012: (Start)

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3); a(0)=1, a(1)=4, a(2)=13.

G.f.: (-x^2 + x - 1)/((x-1)(2*x-1)^2). (End)

Mathematica

Table[3n 2^(n-1)+1, {n, 0, 30}] (* or *) LinearRecurrence[{5, -8, 4}, {1, 4, 13}, 30] (* Harvey P. Dale, Jan 29 2012 *)

Prog

(Magma) [3*n * 2^(n-1) + 1: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011
(PARI) a(n)=3*n*2^(n-1)+1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

n-th difference of a(n), a(n-1), ..., a(0) is (3, 6, 9, ...).

Cf. A134232.

Sequence in context: A299111 A324250 A226866 * A054761 A244197 A300985

Adjacent sequences: A048471 A048472 A048473 * A048475 A048476 A048477

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Better description from Paul Barry, Jul 09 2003

Status

approved