A282023 Start with 1; multiply alternately by 4 and 3.

1, 4, 12, 48, 144, 576, 1728, 6912, 20736, 82944, 248832, 995328, 2985984, 11943936, 35831808, 143327232, 429981696, 1719926784, 5159780352, 20639121408, 61917364224, 247669456896, 743008370688, 2972033482752, 8916100448256, 35664401793024, 106993205379072, 427972821516288

Offset

0,2

Comments

Satisfies Benford's law.

References

Berger, Arno, 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.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for sequences related to Benford's law

Index entries for linear recurrences with constant coefficients, signature (0,12).

Formula

From Ilya Gutkovskiy, Feb 09 2017: (Start)

O.g.f.: (1 + 4*x)/(1 - 12*x^2).

E.g.f.: 2*sinh(2*sqrt(3)*x)/sqrt(3) + 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

CoefficientList[Series[(4 x + 1)/(-12 x^2 + 1), {x, 0, 27}], x] (* or *)
Range[0, 27]! CoefficientList[ Series[2 Sinh[2 Sqrt[3]*x]/Sqrt[3] + Cosh[2 Sqrt[3]*x], {x, 0, 27}], x] (* or *)
LinearRecurrence[{0, 12}, {1, 4}, 28] (* Robert G. Wilson v, Feb 09 2017 *)
nxt[{a_, b_}]:=If[b/a==3, {b, 4b}, {b, 3b}]; NestList[nxt, {1, 4}, 30][[All, 1]] (* Harvey P. Dale, May 31 2020 *)

Prog

(PARI) Vec((1 + 4*x)/(1 - 12*x^2) + O(x^30)) \\ Colin Barker, Feb 09 2017
(PARI) a(n)=2^if(n%2, n+1, n)*3^(n\2) \\ Charles R Greathouse IV, Feb 09 2017

Crossrefs

Cf. A282022.

Sequence in context: A253087 A262414 A081620 * A149376 A149377 A063887

Adjacent sequences: A282020 A282021 A282022 * A282024 A282025 A282026

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 08 2017

Status

approved