A036546 a(n) = T(5,n), array T given by A048471.

1, 33, 129, 417, 1281, 3873, 11649, 34977, 104961, 314913, 944769, 2834337, 8503041, 25509153, 76527489, 229582497, 688747521, 2066242593, 6198727809, 18596183457, 55788550401, 167365651233, 502096953729, 1506290861217, 4518872583681, 13556617751073, 40669853253249

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is 2^(n+4) 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).

Formula

a(n) = 16*3^n - 15. - Ralf Stephan, Feb 17 2004

From Vincenzo Librandi, Nov 11 2011: (Start)

a(n) = 3*a(n-1) + 30.

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

G.f.: (1+29*x)/((1-x)*(1-3*x)). (End)

E.g.f.: exp(x)*(16*exp(2*x) - 15). - Elmo R. Oliveira, Aug 29 2024

Mathematica

LinearRecurrence[{4, -3}, {1, 33}, 30] (* Harvey P. Dale, Mar 16 2012 *)

Prog

(Magma) [16*3^n-15: n in [0..30]]; // Vincenzo Librandi, Nov 11 2011

Crossrefs

Cf. A048471.

Sequence in context: A007419 A158575 A209981 * A043502 A044365 A044746

Adjacent sequences: A036543 A036544 A036545 * A036547 A036548 A036549

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved