A162666 a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

1, 10, 102, 1060, 11204, 120200, 1306008, 14340560, 158822416, 1771073440, 19856872032, 223572243520, 2525471411264, 28599348360320, 324490768902528, 3687079238739200, 41941489422336256, 477496023050283520

Offset

0,2

Comments

Binomial transform of A147960. Tenth binomial transform of A077957.

Links

G. C. Greubel, Table of n, a(n) for n = 0..940

Index entries for linear recurrences with constant coefficients, signature (20,-98).

Formula

a(n) = ((10+sqrt(2))^n + (10-sqrt(2))^n)/2.

G.f.: (1-10*x)/(1-20*x+98*x^2).

E.g.f.: exp(10*x)*cosh(sqrt(2)*x). - Ilya Gutkovskiy, Aug 11 2017

Maple

seq(coeff(series((1-10*x)/(1-20*x+98*x^2), x, n+1), x, n), n = 0..20); # G. C. Greubel, Aug 27 2019

Mathematica

Union[Flatten[NestList[{#[[2]], 20#[[2]]-98#[[1]]}&, {1, 10}, 20]]]  (* Harvey P. Dale, Feb 25 2011 *)
LinearRecurrence[{20, -98}, {1, 10}, 20] (* G. C. Greubel, Aug 27 2019 *)

Prog

(Magma) [ n le 2 select 9*n-8 else 20*Self(n-1)-98*Self(n-2): n in [1..18] ];
(PARI) my(x='x+O('x^20)); Vec((1-10*x)/(1-20*x+98*x^2)) \\ G. C. Greubel, Aug 27 2019
(Sage)
def A162666_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1-10*x)/(1-20*x+98*x^2)).list()
A162666_list(20) # G. C. Greubel, Aug 27 2019
(GAP) a:=[1, 10];; for n in [3..20] do a[n]:=20*a[n-1]-98*a[n-2]; od; a; # G. C. Greubel, Aug 27 2019

Crossrefs

Cf. A147960, A077957.

Sequence in context: A147636 A191014 A147550 * A061630 A062806 A336952

Adjacent sequences: A162663 A162664 A162665 * A162667 A162668 A162669

Keyword

nonn,easy

Author

Klaus Brockhaus, Jul 20 2009

Status

approved