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

0,2

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).

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

Prog

(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

Crossrefs

Cf. A048472.

Sequence in context: A155221 A213569 A299269 * A294837 A117152 A155281

Adjacent sequences: A048474 A048475 A048476 * A048478 A048479 A048480

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved