A083223 a(n) = (5*6^n+(-6)^n)/6.

1, 4, 36, 144, 1296, 5184, 46656, 186624, 1679616, 6718464, 60466176, 241864704, 2176782336, 8707129344, 78364164096, 313456656384, 2821109907456, 11284439629824, 101559956668416, 406239826673664, 3656158440062976, 14624633760251904, 131621703842267136, 526486815369068544

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (0,36).

Formula

a(n) = (5*6^n+(-6)^n)/6.

G.f.: (1+4*x)/((1+6*x)*(1-6*x)).

E.g.f.: (5*exp(6*x)+exp(-6*x))/6.

a(n) = 36*a(n-2). - Wesley Ivan Hurt, Jun 24 2021

From Amiram Eldar, Feb 12 2026: (Start)

Sum_{n>=0} 1/a(n) = 9/7.

Sum_{n>=0} (-1)^n/a(n) = 27/35. (End)

Mathematica

CoefficientList[Series[(1+4x)/((1+6x)(1-6x)), {x, 0, 50}], x]  (* Harvey P. Dale, Mar 01 2011 *)

Prog

(Magma) [(5*6^n+(-6)^n)/6: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011

Crossrefs

Cf. A083222, A083224.

Sequence in context: A035287 A183354 A204504 * A102263 A103931 A334580

Adjacent sequences: A083220 A083221 A083222 * A083224 A083225 A083226

Keyword

easy,nonn

Author

Paul Barry, Apr 23 2003

Status

approved