A165147 a(n) = (3*7^n-3^n)/2.

1, 9, 69, 501, 3561, 25089, 176109, 1234221, 8643921, 60520569, 423683349, 2965901541, 20761665081, 145332718449, 1017332217789, 7121335090461, 49849374331041, 348945706410729, 2442620203155429, 17098342196928981

Offset: 0

Author

Klaus Brockhaus, Sep 15 2009

Keywords

• nonn
• easy

Comments

Partial sums are in A016138.

Binomial transform of A016129. Inverse binomial transform of A165148.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (10,-21).

Crossrefs

Cf. A016138, A016129, A165148.

Programs

Magma

[ (3*7^n-3^n)/2: n in [0..19] ];

Mathematica

LinearRecurrence[{10, -21}, {1, 9}, 25] (* Paolo Xausa, Apr 22 2024 *)
Table[(3*7^n-3^n)/2,{n,0,20}] (* Harvey P. Dale, Aug 05 2025 *)

Formula

a(n) = 10*a(n-1)-21*a(n-2) for n > 1; a(0) = 1, a(1) = 9.

G.f.: (1-x)/((1-3*x)*(1-7*x)).