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A282022 Start with 1; multiply alternately by 3 and 4. 2
1, 3, 12, 36, 144, 432, 1728, 5184, 20736, 62208, 248832, 746496, 2985984, 8957952, 35831808, 107495424, 429981696, 1289945088, 5159780352, 15479341056, 61917364224, 185752092672, 743008370688, 2229025112064, 8916100448256, 26748301344768, 106993205379072, 320979616137216 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Satisfies Benford's law.
LINKS
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.
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
Sequence in context: A344062 A303308 A155714 * A004661 A074430 A064028
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 08 2017
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)