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Fourth column (m=3) of triangle A128494.
3

%I #16 Jul 04 2021 18:58:29

%S 1,1,-3,-3,7,7,-13,-13,22,22,-34,-34,50,50,-70,-70,95,95,-125,-125,

%T 161,161,-203,-203,252,252,-308,-308,372,372,-444,-444,525,525,-615,

%U -615,715,715,-825,-825,946,946,-1078,-1078,1222,1222,-1378,-1378,1547,1547,-1729,-1729,1925,1925,-2135,-2135

%N Fourth column (m=3) of triangle A128494.

%C Unsigned, this is the repeated sequence A002623.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,-4,4,-6,6,-4,4,-1,1).

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

%F a(2*k) = a(2*k+1)= ((-1)^k)*A002623(n), k>=0.

%F a(n) = (-1)^((2*n-1+(-1)^n)/4)*((n+2)*(n+7)*(2*n+9)+3*(n+3)*(n+6)*(-1)^n+12*(-1)^((2*n-1+(-1)^n)/4))/192. - _Luce ETIENNE_, Mar 13 2015

%t CoefficientList[Series[1/((1-x)(1+x^2)^4),{x,0,60}],x] (* or *) LinearRecurrence[{1,-4,4,-6,6,-4,4,-1,1},{1,1,-3,-3,7,7,-13,-13,22},60] (* _Harvey P. Dale_, Jul 04 2021 *)

%o (PARI) Vec(1/((1-x)*(1+x^2)^4) + O(x^50)) \\ _Michel Marcus_, Mar 16 2015

%Y Cf. A008642 (unsigned column m=2). A128499 (column m=4).

%K sign,easy

%O 0,3

%A _Wolfdieter Lang_, Apr 04 2007