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

Author

Klaus Brockhaus, Jul 20 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A147960, A077957.

Programs

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

Magma

[ n le 2 select 9*n-8 else 20*Self(n-1)-98*Self(n-2): n in [1..18] ];

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 *)

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. = PowerSeriesRing(ZZ, prec)
    return P((1-10*x)/(1-20*x+98*x^2)).list()
A162666_list(20) # G. C. Greubel, Aug 27 2019

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