A167032 a(n) = 20*a(n-1) - 64*a(n-2) + 2 for n > 1; a(0) = 1, a(1) = 21.

1, 21, 358, 5818, 93450, 1496650, 23952202, 383258442, 6132227914, 98116017994, 1569857773386, 25117730316106, 401883708825418, 6430139436277578, 102882231360724810, 1646115703292731210, 26337851258768236362

Offset: 0

Author

Klaus Brockhaus, Oct 27 2009

Keywords

• nonn
• easy

Comments

lim_{n -> infinity} a(n)/a(n-1) = 16.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (21,-84,64).

Crossrefs

Cf. A006105, A166915, A166916, A167031, A167033.

Programs

Magma

[ n le 2 select 20*n-19 else 20*Self(n-1)-64*Self(n-2)+2: n in [1..17] ];

Maple

A167032:=n->(257*16^n - 85*4^n + 8)/180: seq(A167032(n), n=0..25); # Wesley Ivan Hurt, May 30 2016

Mathematica

LinearRecurrence[{21, -84, 64}, {1,21,358}, 50] (* G. C. Greubel, May 30 2016 *)
RecurrenceTable[{a[0]==1,a[1]==21,a[n]==20a[n-1]-64a[n-2]+2},a,{n,20}] (* Harvey P. Dale, Oct 27 2019 *)

Formula

a(n) = (257*16^n - 85*4^n + 8)/180.

G.f.: (1+x^2)/((1-x)*(1-4*x)*(1-16*x)).

From G. C. Greubel, May 30 2016: (Start)

a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3) for n>2.

E.g.f.: (1/180)*(257*exp(16*x) - 85*exp(4*x) + 8*exp(x)). (End)