A010035 a(n) = 2*3^(2*n)-3^n.
1, 15, 153, 1431, 13041, 117855, 1062153, 9563751, 86086881, 774821295, 6973509753, 62761942071, 564858541521, 5083730062335, 45753580126953, 411782249840391, 3706040334656961, 33354363270192975, 300189270206577753, 2701703434183722711, 24315330914627073201
Offset: 0
Links
- Delbert L. Johnson, Table of n, a(n) for n = 0..1047
- Index entries for linear recurrences with constant coefficients, signature (12,-27).
Programs
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Maple
f := n->2*3^(2*n)-3^n;
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Mathematica
A010035[n_] := (2*# - 1)*# & [3^n]; Array[A010035, 25, 0] (* or *) LinearRecurrence[{12, -27}, {1, 15}, 25] (* Paolo Xausa, May 28 2025 *)
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PARI
a(n) = 2*3^(2*n)-3^n \\ Michel Marcus, Jun 08 2013
Formula
a(n) = 12*a(n-1)-27*a(n-2). G.f.: (3*x+1) / ((3*x-1)*(9*x-1)). - Colin Barker, Oct 01 2014
Extensions
Revised by N. J. A. Sloane, Jun 10 2013, replacing incorrect definition with formula from Michel Marcus which matches the terms.
More terms, and corrections to name, Maple and prog to agree with the offset, from Colin Barker, Oct 01 2014