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A322039 Expansion of (1 + x)^2 / ((1 - x)^2*(1 + 2*x)^2). 2

%I

%S 1,0,4,-4,16,-28,72,-148,336,-716,1560,-3332,7136,-15164,32168,-67956,

%T 143216,-300972,631096,-1320420,2757376,-5747740,11961544,-24855124,

%U 51574416,-106877068,221210712,-457334468,944495136,-1948642556

%N Expansion of (1 + x)^2 / ((1 - x)^2*(1 + 2*x)^2).

%C Connected with tiling of torus by squares (see A322038).

%H Colin Barker, <a href="/A322039/b322039.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 (-2,3,4,-4).

%F From _Colin Barker_, Dec 04 2018: (Start)

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

%F a(n) = (16 + 11*(-2)^n + 3*(4+(-2)^n)*n) / 27.

%F (End)

%t LinearRecurrence[{-2, 3, 4, -4}, {1, 0, 4, -4}, 100] (* _Amiram Eldar_, Dec 04 2018 *)

%o (PARI) Vec((1 + x)^2 / ((1 - x)^2*(1 + 2*x)^2) + O(x^40)) \\ _Colin Barker_, Dec 04 2018

%Y Cf. A322038, A322040.

%K sign,easy

%O 0,3

%A _N. J. A. Sloane_, Dec 03 2018

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Last modified October 20 22:00 EDT 2021. Contains 348119 sequences. (Running on oeis4.)