A036549 a(n) = T(8,n), array T given by A048471.

1, 257, 1025, 3329, 10241, 30977, 93185, 279809, 839681, 2519297, 7558145, 22674689, 68024321, 204073217, 612219905, 1836659969, 5509980161, 16529940737, 49589822465, 148769467649, 446308403201, 1338925209857, 4016775629825, 12050326889729, 36150980669441

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

n-th difference of a(n), a(n-1), ..., a(0) is 2^(n+7) 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

[128*3^n-127: n in [0..30]]; // Vincenzo Librandi, Nov 11 2011

Formula

From Vincenzo Librandi, Nov 11 2011: (Start)

a(n) = 128*3^n - 127.

a(n) = 3*a(n-1) + 254.

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

G.f.: (1+253*x)/((1-x)*(1-3*x)). (End)

E.g.f.: exp(x)*(128*exp(2*x) - 127). - Elmo R. Oliveira, Aug 29 2024