A084060 - OEIS

%I #22 Mar 05 2023 15:22:05

%S 1,3,-5,9,-11,15,-17,21,-23,27,-29,33,-35,39,-41,45,-47,51,-53,57,-59,

%T 63,-65,69,-71,75,-77,81,-83,87,-89,93,-95,99,-101,105,-107,111,-113,

%U 117,-119,123,-125,129,-131,135,-137,141,-143,147,-149,153,-155,159,-161,165,-167,171,-173,177,-179

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

%C abs(a(n+1)) = A047270(n).

%H Vincenzo Librandi, <a href="/A084060/b084060.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,1,1).

%F Unsigned version is sum of alternate terms of A032766 (numbers congruent to {0,1,3} mod 4): (1, 3, 4, 6, 7, 9, 10, 12, ...) such that a(n) = A032766(n-1) + A032766(n+1). - _Gary W. Adamson_, Sep 13 2007

%F G.f.: (1 + 4*x - 3*x^2 )/( (1-x)*(1+x)^2 ). - _R. J. Mathar_, Oct 25 2011

%F E.g.f.: (1+3*x)*cosh(x) - 3*x*sinh(x). - _G. C. Greubel_, Jan 03 2020

%p seq( (1 + (1-6*n)*(-1)^n)/2, n=0..60); # _G. C. Greubel_, Jan 03 2020

%t Table[(1 + (1-6*n)*(-1)^n)/2, {n,0,60}] (* _G. C. Greubel_, Jan 03 2020 *)

%t LinearRecurrence[{-1,1,1},{1,3,-5},100] (* _Harvey P. Dale_, Mar 05 2023 *)

%o (Magma) [1/2+(1-6*n)*(-1)^n/2: n in [0..60]]; // _Vincenzo Librandi_, Oct 26 2011

%o (PARI) vector(61, n, (1 - (7-6*n)*(-1)^n)/2) \\ _G. C. Greubel_, Jan 03 2020

%o (Sage) [(1 + (1-6*n)*(-1)^n)/2 for n in (0..60)] # _G. C. Greubel_, Jan 03 2020

%o (GAP) List([0..60], n-> (1 + (1-6*n)*(-1)^n)/2) # _G. C. Greubel_, Jan 03 2020

%Y Cf. A032766, A084056.

%K easy,sign

%O 0,2

%A _Paul Barry_, May 11 2003