A036547 a(n) = T(6,n), array T given by A048471.

1, 65, 257, 833, 2561, 7745, 23297, 69953, 209921, 629825, 1889537, 5668673, 17006081, 51018305, 153054977, 459164993, 1377495041, 4132485185, 12397455617, 37192366913, 111577100801, 334731302465, 1004193907457, 3012581722433, 9037745167361, 27113235502145

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

n-th difference of a(n), a(n-1), ..., a(0) is 2^(n+5) 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

[32*3^n-31: n in [0..30]]; // Vincenzo Librandi, Nov 11 2011

Formula

a(n) = 32*3^n - 31. - Ralf Stephan, Feb 17 2004

From Vincenzo Librandi, Nov 11 2011: (Start)

a(n) = 3*a(n-1) + 62.

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

G.f.: (1+61*x)/((1-x)*(1-3*x)). (End)

E.g.f.: exp(x)*(32*exp(2*x) - 31). - Elmo R. Oliveira, Aug 29 2024