A166912 a(n) = 20*a(n-1) - 64*a(n-2) - 225 for n > 2; a(0) = 106, a(1) = 8075, a(2) = 114235.

106, 8075, 114235, 1767675, 28042235, 447713275, 7159562235, 114537594875, 1832539914235, 29320392212475, 469125289738235, 7506000693166075, 120095995320074235, 1921535862038855675, 30744573540292362235

Offset: 0

Author

Klaus Brockhaus, Oct 27 2009

Keywords

• nonn
• easy

Comments

Related to Reverse and Add trajectory of 318 in base 4: A075153(6*n) = 3*a(n).

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (21, -84, 64).

Crossrefs

Cf. A075153, A166913, A166914, A166915, A166916, A166917, A167120, A167121, A167122.

Programs

Mathematica

Join[{106},LinearRecurrence[{21,-84,64},{8075,114235,1767675},20]] (* Harvey P. Dale, Jun 07 2012 *)

PARI

m=15; v=concat([106, 8075, 114235], vector(m-3)); for(n=4, m, v[n]=20*v[n-1]-64*v[n-2]-225); v

Formula

a(n) = (1280*16^n + 940*4^n - 15)/3 for n > 0.

G.f.: (106 + 5849*x - 46436*x^2 + 40256*x^3)/((1-x)*(1-4*x)*(1-16*x)).

From G. C. Greubel, May 28 2016: (Start)

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

E.g.f.: (1/3)*(-15*exp(x) + 940*exp(4*x) + 1280*exp(16*x)) - 629. (End)