A239607 a(n) = (1-2*n^2)^2.
1, 1, 49, 289, 961, 2401, 5041, 9409, 16129, 25921, 39601, 58081, 82369, 113569, 152881, 201601, 261121, 332929, 418609, 519841, 638401, 776161, 935089, 1117249, 1324801, 1560001, 1825201, 2122849, 2455489, 2825761, 3236401, 3690241, 4190209, 4739329
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Mathematica
Table[(1-2*n^2)^2 , {n, 0, 43}] -
PARI
vector(100, n, round(sin(asin(n-1) - acos(n-1))^2)) \\ Colin Barker, May 24 2014
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PARI
a(n)=(1-2*n^2)^2 \\ Charles R Greathouse IV, Jun 04 2014
Formula
From Colin Barker, May 24 2014: (Start)
a(n) = sin(arcsin(n) - arccos(n))^2.
G.f.: -(x^4+44*x^3+54*x^2-4*x+1) / (x-1)^5. (End)
a(n) = A056220(n)^2. - Michel Marcus, May 27 2014
From Amiram Eldar, Mar 11 2022: (Start)
Sum_{n>=0} 1/a(n) = Pi^2*cosec(Pi/sqrt(2))^2/8 + (Pi/(4*sqrt(2))*cot(Pi/sqrt(2))) + 1/2.
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)
E.g.f.: exp(x)*(1 + 24*x^2 + 24*x^3 + 4*x^4). - Stefano Spezia, Feb 22 2025