A171507 a(n) = (5*2^(n+1)-9-(-1)^n)/6-2*n.

0, 0, 1, 6, 17, 42, 93, 198, 409, 834, 1685, 3390, 6801, 13626, 27277, 54582, 109193, 218418, 436869, 873774, 1747585, 3495210, 6990461, 13980966, 27961977, 55924002, 111848053, 223696158, 447392369, 894784794, 1789569645, 3579139350, 7158278761, 14316557586

Offset: 0

Author

Paul Curtz, Dec 10 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3, -1, -3, 2).

Crossrefs

Cf. A042948, A084640.

Programs

Magma

[(5*2^(n+1)-9-(-1)^n)/6 -2*n: n in [0..40]]; // Vincenzo Librandi, Aug 05 2011

Maple

A171507:=n->(5*2^(n+1)-9-(-1)^n)/6 -2*n: seq(A171507(n), n=0..50); # Wesley Ivan Hurt, May 03 2017

Formula

a(n) = 3*a(n-1)-a(n-2)-3*a(n-3)+2*a(n-4). G.f.: x^2*(1+3*x)/((1+x)*(1-2*x)*(1-x)^2).

a(n) = A084640(n) - A042948(n).

a(n+1)-2*a(n) = A042948(n+1).

First differences: a(n+1)-a(n) = A084640(n).

Last digits: a(n) == a(n+10) (mod 10), n>=1.

Extensions

Edited and extended by R. J. Mathar, Dec 15 2009