A048487 a(n) = T(4,n), array T given by A048483.

1, 6, 16, 36, 76, 156, 316, 636, 1276, 2556, 5116, 10236, 20476, 40956, 81916, 163836, 327676, 655356, 1310716, 2621436, 5242876, 10485756, 20971516, 41943036, 83886076, 167772156, 335544316, 671088636, 1342177276, 2684354556, 5368709116, 10737418236, 21474836476

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Row sums of triangle A131113. - Gary W. Adamson, Jun 15 2007

a(n) = sum of (n+1)-th row terms of triangle A134636. This sequence is the binomial transform of 1, 5, 5, (5 continued). - Gary W. Adamson, Nov 04 2007

Row sums of triangle A135856. - Gary W. Adamson, Dec 01 2007

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A010716 (n-th difference of a(n), a(n-1), ..., a(0)).

Diagonal of A062001.

A column of A119726.

Cf. A048483, A123208, A131113, A134636, A135856.

Programs

Magma

[5*2^n-4: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011

Mathematica

a=1; lst={a}; k=5; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 15 2008 *)
a=6; lst={1, a}; k=10; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)

Formula

a(n) = 5*2^n - 4. - Henry Bottomley, May 29 2001

a(n) = 2*a(n-1) + 4 for n > 0 with a(0) = 1. - Paul Barry, Aug 25 2004

From Colin Barker, Sep 13 2012: (Start)

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

G.f.: (1 + 3*x)/((1 - x)*(1 - 2*x)). (End)

a(n) = A123208(2*n). - Philippe Deléham, Apr 15 2013

E.g.f.: exp(x)*(5*exp(x) - 4). - Stefano Spezia, Oct 03 2023