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

0,3

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).

Formula

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

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)

Mathematica

Table[(1-2*n^2)^2 , {n, 0, 43}]

Prog

(PARI) vector(100, n, round(sin(asin(n-1) - acos(n-1))^2)) \\ Colin Barker, May 24 2014
(PARI) a(n)=(1-2*n^2)^2 \\ Charles R Greathouse IV, Jun 04 2014

Crossrefs

Cf. A056220, A239608, A239609, A239610.

Sequence in context: A144407 A089552 A017354 * A227079 A251222 A250967

Adjacent sequences: A239604 A239605 A239606 * A239608 A239609 A239610

Keyword

nonn,easy

Author

José María Grau Ribas, Mar 22 2014

Status

approved