A163114 a(n) = 5*a(n-2) for n > 2; a(1) = 3, a(2) = 5.

3, 5, 15, 25, 75, 125, 375, 625, 1875, 3125, 9375, 15625, 46875, 78125, 234375, 390625, 1171875, 1953125, 5859375, 9765625, 29296875, 48828125, 146484375, 244140625, 732421875, 1220703125, 3662109375, 6103515625, 18310546875

Offset

1,1

Comments

Binomial transform is A163062, second binomial transform is A163063, third binomial transform is A098648 without initial 1, fourth binomial transform is A163064, fifth binomial transform is A163065.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,5).

Formula

a(n) = (2-(-1)^n)*5^(1/4*(2*n-1+(-1)^n)).

G.f.: x*(3+5*x)/(1-5*x^2).

a(n) = A056487(n), n>=1.

E.g.f.: cosh(sqrt(5)*x) + 3*sinh(sqrt(5)*x)/sqrt(5) - 1. - Stefano Spezia, Nov 19 2023

Mathematica

CoefficientList[Series[x*(3 + 5*x)/(1 - 5*x^2), {x, 0, 50}], x] (* G. C. Greubel, Dec 21 2017 *)
LinearRecurrence[{0, 5}, {3, 5}, 30] (* Harvey P. Dale, Aug 01 2021 *)

Prog

(Magma) [ n le 2 select 2*n+1 else 5*Self(n-2): n in [1..29] ];
(PARI) x='x+O('x^30); Vec(x*(3+5*x)/(1-5*x^2)) // G. C. Greubel, Dec 21 2017

Crossrefs

Cf. A056487, A098648, A163062, A163063, A163064, A163065.

Sequence in context: A018272 A328834 A018421 * A111386 A056487 A146582

Adjacent sequences: A163111 A163112 A163113 * A163115 A163116 A163117

Keyword

nonn,easy

Author

Klaus Brockhaus, Jul 21 2009

Status

approved