A133647 A133566 * A000244.
1, 3, 12, 27, 108, 243, 972, 2187, 8748, 19683, 78732, 177147, 708588, 1594323, 6377292, 14348907, 57395628, 129140163, 516560652, 1162261467, 4649045868, 10460353203, 41841412812, 94143178827, 376572715308, 847288609443, 3389154437772, 7625597484987, 30502389939948
Offset: 0
Examples
a(3) = 27 = 3^3. a(4) = 108 = 4 * 3^3.
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,9).
Programs
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Mathematica
Join[{1},Flatten[NestList[9#&,{3,12},20]]] (* or *) LinearRecurrence[{0,9},{1,3,12},40] (* Harvey P. Dale, Aug 01 2019 *)
Formula
A133566 * A000244, where A133566 = an infinite lower triangular matrix and A000244 = [3^0, 3^1, 3^2, ...]. For odd n, a(n) = 3^n. For even n, a(n) = 4 * 3^(n-1).
From Philippe Deléham, Apr 06 2012: (Start)
G.f.: (1+3*x+3*x^2)/(1-9*x^2).
a(n+2) = 9*a(n), a(0) = 1, a(1) = 3, a(2) = 12. (End)
From Amiram Eldar, Jun 02 2025: (Start)
Sum_{n>=0} 1/a(n) = 47/32.
Sum_{n>=0} (-1)^n/a(n) = 23/32. (End)
Extensions
More terms from Philippe Deléham, Apr 06 2012
Comments