A036545 a(n) = T(4,n), array T given by A048471.

1, 17, 65, 209, 641, 1937, 5825, 17489, 52481, 157457, 472385, 1417169, 4251521, 12754577, 38263745, 114791249, 344373761, 1033121297, 3099363905, 9298091729, 27894275201, 83682825617, 251048476865, 753145430609, 2259436291841, 6778308875537, 20334926626625

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

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

[8*3^n-7: n in [0..30]]; // Vincenzo Librandi, Nov 11 2011

Mathematica

LinearRecurrence[{4,-3},{1,17},30] (* Harvey P. Dale, Mar 05 2022 *)

Formula

a(n) = 8*3^n - 7. - Ralf Stephan, Feb 17 2004

From Vincenzo Librandi, Nov 11 2011: (Start)

a(n) = 3*a(n-1) + 14.

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

G.f.: (1+13*x)/((1-x)*(1-3*x)). (End)

E.g.f.: exp(x)*(8*exp(2*x) - 7). - Elmo R. Oliveira, Aug 29 2024