A274074 a(n) = 6^n+(-1)^n.

2, 5, 37, 215, 1297, 7775, 46657, 279935, 1679617, 10077695, 60466177, 362797055, 2176782337, 13060694015, 78364164097, 470184984575, 2821109907457, 16926659444735, 101559956668417, 609359740010495, 3656158440062977, 21936950640377855, 131621703842267137

Offset

0,1

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1285

Weerayuth Nilsrakoo and Achariya Nilsrakoo, On One-Parameter Generalization of Jacobsthal Numbers, WSEAS Trans. Math. (2025) Vol. 24, 51-61. See p. 3.

Index entries for linear recurrences with constant coefficients, signature (5,6).

Formula

O.g.f.: (2-5*x) / ((1+x)*(1-6*x)).

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

a(n) = 5*a(n-1)+6*a(n-2) for n>1.

Mathematica

Array[6^# + (-1)^# &, 23, 0] (* or *)
LinearRecurrence[{5, 6}, {2, 5}, 23] (* or *)
CoefficientList[ Series[(5x -2)/(6x^2 + 5x -1), {x, 0, 23}], x] (* Robert G. Wilson v, Jan 01 2017 *)

Prog

(PARI) Vec((2-5*x)/((1+x)*(1-6*x)) + O(x^30))

Crossrefs

Sequences of the type k^n+(-1)^n: A014551 (k=2), A102345 (k=3), A201455 (k=4), A087404 (k=5), this sequence (k=6).

Sequence in context: A089195 A067464 A081545 * A097496 A099657 A107633

Adjacent sequences: A274071 A274072 A274073 * A274075 A274076 A274077

Keyword

nonn,easy,changed

Author

Colin Barker, Jun 09 2016

Status

approved