A177143 Pasquale's sequence: a(n) = 2a(n-1) + (-1)^n*floor(n/2), with a(1)=1.

1, 3, 5, 12, 22, 47, 91, 186, 368, 741, 1477, 2960, 5914, 11835, 23663, 47334, 94660, 189329, 378649, 757308, 1514606, 3029223, 6058435, 12116882, 24233752, 48467517, 96935021, 193870056, 387740098, 775480211, 1550960407, 3101920830, 6203841644, 12407683305

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,3,-1,-2).

Formula

a(n) = 2*a(n-1) + n/2 if n is even; a(n) = 2*a(n-1) - (n-1)/2 if n is odd, with a(1)=1. - Vincenzo Librandi, Sep 30 2010

G.f.: -x*(-1-2*x+x^2+x^3) / ( (2*x-1)*(x-1)*(1+x)^2 ). - R. J. Mathar, Nov 18 2010

a(n) = 13*2^n/18 - 1/4 + (-1)^n*(n/6+1/36) = a(n-1) + 3*a(n-2) - a(n-3) - 2*a(n-4). - R. J. Mathar, Nov 18 2010

Mathematica

LinearRecurrence[{1, 3, -1, -2}, {1, 3, 5, 12}, 50] (* Paolo Xausa, Jan 04 2024 *)

Prog

(PARI) Vec(-x*(-1-2*x+x^2+x^3)/((2*x-1)*(x-1)*(1+x)^2) + O(x^40)) \\ Michel Marcus, Aug 15 2015
(PARI) first(m)=my(v=vector(m)); v[1]=1; for(i=2, m, v[i]=2*v[i-1]+(-1)^i*floor(i/2)); v; \\ Anders Hellström, Aug 15 2015

Crossrefs

Sequence in context: A263346 A034763 A183921 * A191391 A121482 A368858

Adjacent sequences: A177140 A177141 A177142 * A177144 A177145 A177146

Keyword

nonn,easy

Author

Robert Wainwright (RWainwright(AT)Iona.edu), May 03 2010

Extensions

Edited by N. J. A. Sloane, May 06 2010

Status

approved