A166754 - OEIS

%I #19 Sep 08 2022 08:45:48

%S 1,2,9,22,53,114,241,494,1005,2026,4073,8166,16357,32738,65505,131038,

%T 262109,524250,1048537,2097110,4194261,8388562,16777169,33554382,

%U 67108813,134217674,268435401,536870854,1073741765,2147483586

%N a(n) = 4*A061547(n+1) - 3*A166753(n).

%H G. C. Greubel, <a href="/A166754/b166754.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,2).

%F G.f.: (1-x+4*x^2)/((1+x)*(1-x)^2*(1-2*x)).

%F a(n) = (2^(n+3) + (-1)^n - (4*n+7))/2.

%F a(n) = A000975(n) - 4*A011377(n-2).

%F a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4).

%F E.g.f.: (8*exp(2*x) + exp(-x) - (4*x+7)*exp(x))/2. - _G. C. Greubel_, Jun 04 2019

%t LinearRecurrence[{3,-1,-3,2}, {1,2,9,22}, 40] (* _G. C. Greubel_, May 24 2016 *)

%o (PARI) my(x='x+O('x^40)); Vec((1-x+4*x^2)/((1+x)*(1-x)^2*(1-2*x))) \\ _G. C. Greubel_, Oct 10 2017

%o (Magma) [(2^(n+3) +(-1)^n -(4*n+7))/2: n in [0..40]]; // _G. C. Greubel_, Oct 10 2017

%o (Sage) [(2^(n+3) + (-1)^n - (4*n+7))/2 for n in (0..40)] # _G. C. Greubel_, Jun 04 2019

%o (GAP) List([0..40], n-> (2^(n+3) + (-1)^n - (4*n+7))/2) # _G. C. Greubel_, Jun 04 2019

%Y Cf. A061547, A166753.

%Y Cf. A000975, A011377.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Oct 21 2009