A165470 a(0)=1, a(1)=5, a(n) = 20*a(n-2) - a(n-1).

1, 5, 15, 85, 215, 1485, 2815, 26885, 29415, 508285, 80015, 10085685, -8485385, 210199085, -379906785, 4583888485, -12182024185, 103859793885, -347500277585, 2424696155285, -9374701706985, 57868624812685, -245362658952385, 1402735155206085, -6309988334253785

Offset

0,2

Comments

a(n)/a(n-1) tends to -5.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,20).

Formula

G.f.: (1+6*x)/(1+x-20*x^2).

a(n) = Sum_{k=0..n} A112555(n,k)*4^k.

a(n) = (10*4^n-(-5)^n)/9. - Klaus Brockhaus, Sep 25 2009

E.g.f.: (10*exp(4*x) - exp(-5*x))/9. - G. C. Greubel, Oct 20 2018

Maple

seq(coeff(series((1+6*x)/(1+x-20*x^2), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 21 2018

Mathematica

LinearRecurrence[{-1, 20}, {1, 5}, 40] (* G. C. Greubel, Oct 20 2018 *)

Prog

(PARI) vector(40, n, n--; (10*4^n-(-5)^n)/9) \\ G. C. Greubel, Oct 20 2018
(Magma) [(10*4^n-(-5)^n)/9: n in [0..40]]; // G. C. Greubel, Oct 20 2018
(Python) for n in range(0, 30): print(int((10*4**n-(-5)**n)/9), end=', ') # Stefano Spezia, Oct 21 2018
(GAP) a:=[1, 5];; for n in [3..25] do a[n]:=20*a[n-2]-a[n-1]; od; a; # Muniru A Asiru, Oct 21 2018

Crossrefs

Sequence in context: A183937 A275971 A030487 * A165625 A058820 A054363

Adjacent sequences: A165467 A165468 A165469 * A165471 A165472 A165473

Keyword

easy,sign

Author

Philippe Deléham, Sep 20 2009

Status

approved