A234255 Decimal expansion of -B(12) = 691/2730, 13th Bernoulli number without sign.
0, 2, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5
Offset: 1
Examples
0.2531135531135531135531135531135531135531135...
Links
- Index entries for linear recurrences with constant coefficients, signature (2,-2,1).
Crossrefs
Programs
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Magma
[0,2] cat &cat [[5, 3, 1, 1, 3, 5]^^30]; // Wesley Ivan Hurt, Jun 28 2016
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Maple
A234255:=n->[5, 3, 1, 1, 3, 5][(n mod 6)+1]: 0,2,seq(A234255(n), n=0..100); # Wesley Ivan Hurt, Jun 28 2016
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Mathematica
Join[{0},RealDigits[-BernoulliB[12],10,120][[1]]] (* or *) PadRight[{0,2}, 120, {3,5,5,3,1,1}] (* Harvey P. Dale, Dec 30 2013 *) -
PARI
default(realprecision, 120); -bernfrac(12) + 0. \\ Rick L. Shepherd, Jan 15 2014
Formula
From Chai Wah Wu, Jun 04 2016: (Start)
a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) for n > 5.
G.f.: x^2*(2 + x - 3*x^2 + 3*x^3)/((1 - x)*(1 - x + x^2)). (End)
From Wesley Ivan Hurt, Jun 28 2016: (Start)
a(n) = a(n-6) for n>8.
a(n) = (9 - 6*cos(n*Pi/3) + 2*sqrt(3)*sin(n*Pi/3))/3 for n>2. (End)
Extensions
Offset corrected by and more terms from Rick L. Shepherd, Jan 15 2014
Comments