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A140230 Binomial transform of [1, 2, -3, -4, 5, 6, -7, -8, 9, 10,...]. 3

%I

%S 1,3,2,-6,-20,-28,-8,56,144,176,32,-352,-832,-960,-128,1920,4352,4864,

%T 512,-9728,-21504,-23552,-2048,47104,102400,110592,8192,-221184,

%U -475136,-507904,-32768,1015808,2162688,2293760,131072,-4587520,-9699328

%N Binomial transform of [1, 2, -3, -4, 5, 6, -7, -8, 9, 10,...].

%H Vincenzo Librandi, <a href="/A140230/b140230.txt">Table of n, a(n) for n = 1..206</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (4,-8,8,-4).

%F A007318 * [1, 2, -3, -4, 5, 6, -7, -8, 9, 10,...]; i.e. (+) signs when n == 1 or 2 MOD 4; (-) otherwise.

%F a(1+4*n) + a(2+4*n) + a(3+4*n) + a(4+4*n) = 0. - _Paul Curtz_, Apr 22 2011

%F a(n) = +4*a(n-1) -8*a(n-2) +8*a(n-3) -4*a(n-4). _Joerg Arndt_, Apr 25 2011

%F G.f. x*(x-1)*(2*x^2-1) / (1-2*x+2*x^2)^2 . - _R. J. Mathar_, Jun 02 2011

%e a(4) = -6 = (1, 3, 3, 1) dot (1, 2, -3, -4) = (1 + 6 - 9 - 4).

%o (PARI) Vec((2*x^3-2*x^2-x+1)/(4*x^4-8*x^3+8*x^2-4*x+1)+O(x^66)) /* Joerg Arndt, Apr 25 2011 */

%K sign,easy

%O 1,2

%A _Gary W. Adamson_, May 13 2008

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Last modified June 24 11:45 EDT 2021. Contains 345416 sequences. (Running on oeis4.)