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%I #29 Mar 11 2022 07:30:13
%S 1,1,49,289,961,2401,5041,9409,16129,25921,39601,58081,82369,113569,
%T 152881,201601,261121,332929,418609,519841,638401,776161,935089,
%U 1117249,1324801,1560001,1825201,2122849,2455489,2825761,3236401,3690241,4190209,4739329
%N a(n) = (1-2*n^2)^2.
%H Colin Barker, <a href="/A239607/b239607.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 (5,-10,10,-5,1).
%F a(n) = sin(arcsin(n) - arccos(n))^2. G.f.: -(x^4+44*x^3+54*x^2-4*x+1) / (x-1)^5. - _Colin Barker_, May 24 2014
%F a(n) = A056220(n)^2. - _Michel Marcus_, May 27 2014
%F From _Amiram Eldar_, Mar 11 2022: (Start)
%F Sum_{n>=0} 1/a(n) = Pi^2*cosec(Pi/sqrt(2))^2/8 + (Pi/(4*sqrt(2))*cot(Pi/sqrt(2))) + 1/2.
%F Sum_{n>=0} (-1)^n/a(n) = Pi^2*cosec(Pi/sqrt(2))*cot(Pi/sqrt(2))/8 + (Pi/(4*sqrt(2)))*cosec(Pi/sqrt(2)) + 1/2. (End)
%t Table[(1-2*n^2)^2 , {n, 0, 43}]
%o (PARI) vector(100, n, round(sin(asin(n-1) - acos(n-1))^2)) \\ _Colin Barker_, May 24 2014
%o (PARI) a(n)=(1-2*n^2)^2 \\ _Charles R Greathouse IV_, Jun 04 2014
%Y Cf. A056220, A239608, A239609, A239610.
%K nonn,easy
%O 0,3
%A _José María Grau Ribas_, Mar 22 2014
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