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

Author

Klaus Brockhaus, Jul 21 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A056487, A098648, A163062, A163063, A163064, A163065, A111386.

Programs

Magma

[ n le 2 select 2*n+1 else 5*Self(n-2): n in [1..29] ];

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 *)

PARI

x='x+O('x^30); Vec(x*(3+5*x)/(1-5*x^2)) \\ G. C. Greubel, Dec 21 2017

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