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Expansion of (x^6 - x^4 + x^3 - x - 1)/((x - 1)^3*(x + 1)^2).
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%I #13 Dec 22 2023 11:55:50

%S 1,2,4,5,9,10,15,16,22,23,30,31,39,40,49,50,60,61,72,73,85,86,99,100,

%T 114,115,130,131,147,148,165,166,184,185,204,205,225,226,247,248,270,

%U 271,294,295,319,320,345,346,372,373,400,401,429,430,459,460,490,491,522,523,555,556,589,590,624

%N Expansion of (x^6 - x^4 + x^3 - x - 1)/((x - 1)^3*(x + 1)^2).

%D Mark Thomas, Email to N. J. A. Sloane, Mar 03 2017

%H Colin Barker, <a href="/A282737/b282737.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).

%F From _Colin Barker_, Mar 04 2017: (Start)

%F a(n) = (n^2 + 14*n) / 8 for n>1 and even.

%F a(n) = (n^2 + 12*n - 5) / 8 for n>1 and odd.

%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4. (End)

%o (PARI) Vec((x^6 - x^4 + x^3 - x - 1)/((x - 1)^3*(x + 1)^2) + O(x^60)) \\ _Colin Barker_, Mar 04 2017

%Y First differences give A282738.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Mar 04 2017