A048477 a(n) = T(5,n), array T given by A048472.

1, 7, 25, 73, 193, 481, 1153, 2689, 6145, 13825, 30721, 67585, 147457, 319489, 688129, 1474561, 3145729, 6684673, 14155777, 29884417, 62914561, 132120577, 276824065, 578813953, 1207959553, 2516582401, 5234491393, 10871635969, 22548578305, 46707769345

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (6, 12, 18, ...).

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

Cf. A048472.

Programs

Magma

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

PARI

{a(n) = if( n<0, 0, 3 * n * 2^n + 1)}; /* Michael Somos, May 13 2014 */

PARI

Vec((1+2*x-2*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Feb 18 2016

Formula

a(n) = 6*n * 2^(n-1) + 1.

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

a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3) for n>2. - Colin Barker, Feb 18 2016