A036548 a(n) = T(7,n), array T given by A048471.

1, 129, 513, 1665, 5121, 15489, 46593, 139905, 419841, 1259649, 3779073, 11337345, 34012161, 102036609, 306109953, 918329985, 2754990081, 8264970369, 24794911233, 74384733825, 223154201601, 669462604929, 2008387814913, 6025163444865, 18075490334721, 54226471004289

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

n-th difference of a(n), a(n-1), ..., a(0) is 2^(n+6) for n=1, 2, 3, ...

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Crossrefs

Cf. A048471.

Programs

Magma

[64*3^n-63: n in [0..30]]; // Vincenzo Librandi, Nov 11 2011

Formula

a(n) = 64*3^n - 63. - Ralf Stephan, Feb 17 2004

From Vincenzo Librandi, Nov 11 2011: (Start)

a(n) = 3*a(n-1) + 126.

a(n) = 4*a(n-1) - 3*a(n-2).

G.f.: (1+125*x)/((1-x)*(1-3*x)). (End)

E.g.f.: exp(x)*(64*exp(2*x) - 63). - Elmo R. Oliveira, Aug 29 2024