A241888 a(n) = 2^(4*n + 1) - 1.

1, 31, 511, 8191, 131071, 2097151, 33554431, 536870911, 8589934591, 137438953471, 2199023255551, 35184372088831, 562949953421311, 9007199254740991, 144115188075855871, 2305843009213693951, 36893488147419103231, 590295810358705651711, 9444732965739290427391

Offset

0,2

Links

Jens Kruse Andersen, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (17,-16).

Formula

a(n) = 2^(4*n + 1) - 1 = A000225(4*n + 1) = A013776(n) - 1 = 4*A000225(4*n - 1) + 3.

a(n) = 17*a(n-1) - 16*a(n-2). - Colin Barker, Aug 31 2014

G.f.: (14*x+1) / ((x-1)*(16*x-1)). - Colin Barker, Aug 31 2014

Maple

seq(coeff(series((14*x+1)/((x-1)*(16*x-1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Mar 12 2019

Mathematica

Table[2^(4n + 1) - 1, {n, 0, 29}]
CoefficientList[ Series[(14x + 1)/((x - 1) (16x - 1)), {x, 0, 18}], x] (* Robert G. Wilson v, Jan 28 2015 *)
LinearRecurrence[{17, -16}, {1, 31}, 30] (* Harvey P. Dale, Mar 13 2016 *)

Prog

(PARI) vector(40, n, 2^(4*n-3)-1) \\ Derek Orr, Aug 11 2014
(PARI) Vec((14*x+1)/((x-1)*(16*x-1)) + O(x^100)) \\ Colin Barker, Aug 31 2014
(GAP) List([0..20], n->2^(4*n+1)-1); # Muniru A Asiru, Mar 12 2019

Crossrefs

Cf. A000225, A004171, A013776.

Sequence in context: A022595 A125488 A319427 * A316457 A278558 A022659

Adjacent sequences: A241885 A241886 A241887 * A241889 A241890 A241891

Keyword

nonn,easy

Author

Wassan Letourneur, Aug 09 2014

Status

approved