A162667 a(n) = 20*a(n-1) - 97*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

1, 10, 103, 1090, 11809, 130450, 1463527, 16616890, 190375681, 2195675290, 25447064743, 295960791730, 3450850554529, 40308814292770, 471443782066087, 5518920654923050, 64648366238050561, 757632021233475370

Offset: 0

Author

Klaus Brockhaus, Jul 15 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A152056. Tenth binomial transform of powers of 3 interleaved with zeros.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..930
• Index entries for linear recurrences with constant coefficients, signature (20,-97).

Crossrefs

Cf. A152056, A000244 (powers of 3).

Programs

GAP

a:=[1,10];; for n in [3..20] do a[n]:=20*a[n-1]-97*a[n-2]; od; a; # G. C. Greubel, Aug 27 2019

Magma

[ n le 2 select 9*n-8 else 20*Self(n-1)-97*Self(n-2): n in [1..18] ];

Maple

seq(coeff(series((1-10*x)/(1-20*x+97*x^2), x, n+1), x, n), n = 0..20); # G. C. Greubel, Aug 27 2019

Mathematica

LinearRecurrence[{20,-97}, {1,10}, 20] (* G. C. Greubel, Aug 27 2019 *)

PARI

my(x='x+O('x^20)); Vec((1-10*x)/(1-20*x+97*x^2)) \\ G. C. Greubel, Aug 27 2019

Sage

def A162667_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1-10*x)/(1-20*x+97*x^2)).list()
A162667_list(20) # G. C. Greubel, Aug 27 2019

Formula

a(n) = ((10+sqrt(3))^n + (10-sqrt(3))^n)/2.

G.f.: (1-10*x)/(1-20*x+97*x^2).