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

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

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

Cf. A134232.

Programs

Magma

[3*n * 2^(n-1) + 1: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011

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 *)

PARI

a(n)=3*n*2^(n-1)+1 \\ Charles R Greathouse IV, Oct 07 2015

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)

Extensions

Better description from Paul Barry, Jul 09 2003