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
Links
- Jens Kruse Andersen, Table of n, a(n) for n = 0..100
- Index entries for linear recurrences with constant coefficients, signature (17,-16).
Programs
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GAP
List([0..20],n->2^(4*n+1)-1); # Muniru A Asiru, Mar 12 2019
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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
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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 *) -
PARI
vector(40, n, 2^(4*n-3)-1) \\ Derek Orr, Aug 11 2014
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PARI
Vec((14*x+1)/((x-1)*(16*x-1)) + O(x^100)) \\ Colin Barker, Aug 31 2014
Formula
From Colin Barker, Aug 31 2014: (Start)
a(n) = 17*a(n-1) - 16*a(n-2).
G.f.: (14*x+1)/((x-1)*(16*x-1)). (End)
E.g.f.: exp(x)*(2*exp(15*x) - 1). - Elmo R. Oliveira, Feb 20 2025