OFFSET
0,2
COMMENTS
Satisfies Benford's law.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Arno Berger and Theodore P. Hill, Benford's law strikes back: no simple explanation in sight for mathematical gem, The Mathematical Intelligencer 33.1 (2011): 85-91. Also at CalPoly.
Index entries for linear recurrences with constant coefficients, signature (0,12).
FORMULA
From Ilya Gutkovskiy, Feb 09 2017: (Start)
O.g.f.: (1 + 3*x)/(1 - 12*x^2).
E.g.f.: sqrt(3)*sinh(2*sqrt(3)*x)/2 + cosh(2*sqrt(3)*x).
(End)
From Colin Barker, Feb 09 2017: (Start)
a(n) = 2^n * 3^(n/2) for n even.
a(n) = 2^(n-1) * 3^((n+1)/2) for n odd.
a(n) = 12*a(n-2) for n>1.
(End)
MATHEMATICA
LinearRecurrence[{0, 12}, {1, 3}, 30] (* Harvey P. Dale, Jun 19 2021 *)
PROG
(PARI) Vec((1 + 3*x) / (1 - 12*x^2) + O(x^30)) \\ Colin Barker, Feb 09 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 08 2017
STATUS
approved